CBSE Class 8

RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.6

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.6

Other Exercises

• RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.1
• RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.2
• RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.3
• RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.4
• RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.5
• RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.6
• RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.7
• RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.8
• RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.9

Factorize each of the following algebraic expressions :
Question 1.
4x² + 12xy + 9y²
Solution:
4x² + 12xy + 9y² = (2x)² + 2 x 2x x 3y + (3y)² {∵ a² + 2ab + b² = (a +b)²}
= (2x + 3y)²    

Question 2.
9a² – 24ab + 16b²
Solution:
9a² – 24ab + 16b²
= (3a)² – 2 x 3a x 4b + (4b)²     {∵ a² – 2ab + b² = (a – b)²}
= (3a – 4b)²

Question 3.
36a² – 6pqr + 9r²
Solution:
p²q² – 6pqr + 9r²
= (pq)² – 2 x pq x3r + (3r)² {∵ a² – 2ab + b² = (a -b)²}
= (pq-3r)²

Question 4.
36a² + 36a + 9
Solution:
36a² + 36a + 9
= (6a)² + 2 x 6a x 3 + (3)²   {∵ a² + 2ab + b² = (a + b)²
= (6a + 3)²

Question 5.
a² + 2ab + b² – 16
Solution:
a² + 2ab + b² – 16
= (a + b)² – (4)²     {∵ a² + 2ab + b² = (a + b)² and a² – b² = (a + b) (a – b)}
= (a + b + 4) (a + b – 4)

Question 6.
9z² – x² + 4xy – 4y²
Solution:
9z² – x² + 4xy – 4y²    {∵ a² – b² = (a + b) (a – b) and a² – 2ab + b² (a – b)²}
= 9z² – (x² – 4xy + 4y²)
= (3z)² – [(x)² – 2 x x x 2y + (2y)²]
= (3z)²-(x-2y)²
= (3z + x – 2y) (3z – x + 2y)

Question 7.
9a⁴ – 24a²b² + 16b⁴ – 256
Solution:

Question 8.
16 – a⁶ + 4a³b³ – 4b⁶
Solution:

Question 9.
a² – 2ab + b² – c²
Solution:

Question 10.
x² + 2x + 1 – 9y²
Solution:

Question 11.
a² + 4ab + 3b²
Solution:
a² + 4ab + 3b²
= a² + 4ab+ 4b² – b²
= (a)² + 2 x a x 2b + (2b)² – b² (∵ 3b² = 4b² – b²)
= (a + 2b)² – (b)²   {∵ a² – b² = (a +b) (a – b)}
= (a + 2b + b) (a + 2b- b)

Question 12.
96 – 4x-x²
Solution:
96 – 4x – x² = 96 – (4x + x²)
= 96 – [(x)² + 2 x x x 2 + (2)²] + (2)²   (on completing the square)
= 96 + 4 – (x + 2)² = 100 – (x + 2)²
= (10)² – (x + 2)²
= (10 + x + 2) (10 – x- 2)
= (x + 12) (-x + 8)

Question 13.
a⁴ + 3a² + 4
Solution:
a⁴ + 3a² + 4
= (a²)² + (2)² + 2 x a² x 2 – a²   (on completing the square)
= (a² + 2)² – (a)²
= (a² + 2 + a) (a² + 2 – a)
= (a¹ + a + 2) (a² – a + 2)

Question 14.
4a⁴ + 1
Solution:
4x⁴ + 1 = (2a²)² + (1)² + 2 x 2x² x 1 – 2 x 2x² x 1  (completing the square)
= (2x² + 1)² – 4a²
= (2x² + 1)² – (2a)²   {a² – b² = (a + b) (a – b)}
= (2x² + 1 + 2a) (2a² + 1 – 2a)
= (2a² + 2a + 1) (2a² – 2a + 1)

Question 15.
4x⁴+y⁴
Solution:
4a⁴ + y⁴ = (2x²)² + (y²)² + 2 x 2x²y² – 2 x 2x²y²
= (2x² + y²)² – 4x²y²
= (2x² + y²)² – (2xy)²
= (2x² + y² + 2xy) (2x² + y² – 2xy)
= (2x² + 2xy + y²) (2x² – 2xy + y²)

Question 16.
(x+ 2)² – 6 (a + 2) + 9
Solution:
(x + 2)² – 6 (x + 2) + 9
=  (x + 2)² – 2 x (x + 2) x 3 + (3)²
= (x + 2 – 3)²
= (x-1)² = (x-1)(x-1)

Question 17.
25 – p² – q² – 2pq
Solution:

Question 18.
a² + 9y² – 6xy – 25a²
Solution:
a² + 9y² – 6xy – 25a²

Question 19.
49 – a² + 8ab – 16b²
Solution:

Question 20.
a² – 8ab + 16b² – 25c²
Solution:

Question 21.
x² -y²+ 6y- 9
Solution:

Question 22.
25x² – 10x + 1 – 36y²
Solution:

Question 23.
a²-b² + 2bc – c²
Solution:

Question 24.
a² + 2ab + b² -c²
Solution:

Question 25.
49 -x² – y² + 2xy
Solution:

Question 26.
a² + 4b² – 4ab – 4c²
Solution:

Question 27.
x² -y² – 4xz + 4z²
Solution:

Hope given RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.6 are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.2

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.2

Other Exercises

• RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.1
• RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.2
• RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.3
• RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4
• RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.5
• RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.6

Divide :

Question 1.
6x³y²z² by 3x²yz
Solution:

Question 2.
15m²n³ by 5m²n²
Solution:

Question 3.
24a³b³ by -8ab
Solution:

Question 4.
-21abc² by 7abc
Solution:

Question 5.
72xyz² by – 9xz
Solution:

Question 6.
-72a⁴b⁵c⁸ by – 9a²b²c³
Solution:

Simplify :

Question 7.

Solution:

Question 8.

Solution:

Hope given RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.2 are helpful to complete your math homework.

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RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.1

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.1

Other Exercises

• RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.1
• RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.2
• RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.3
• RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4
• RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.5
• RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.6

Question 1.
Write the degree of each of the following polynomials :
(i) 2x³+5x²-7
(ii) 5x² – 3x +7 ’
(iii) 2x + x² –-8
(iv) \(\frac { 1 }{ 2 }\) y⁷ -12y⁵ + 48y⁶ – 10
(v) 3x³ + 1
(vi) 5
(vii) 20x³ + 12x²y²– 10y² + 20
Solution:
(i) 2x³ + 5x²-7: The degree of this polynomial is 3.
(ii) 5x² – 3x + 2 : The degree of this polynomial is 2.
(iii) 2x + x² – 8 : The degree of this polynomial is 2.
(iv) \(\frac { 1 }{ 2 }\) y⁷ – 12y⁶ + 48y⁵ – 10 : The degree of this polynomial is 7.
(v) 3x³ + 1 : The degree of this polynomial is 3.
(vi) 5 : The degree of this polynomial is 0 as it is only constant term
(vii) 20x³ + 12x²y² – 10y² + 20: The degree of this polynomial is 2 + 2 = 4.

Question 2.
Which of the following expressions are not polynomials :
(i) x² + 2x²                   
(ii) √a x + x²-x³
(iii) 3y³ – √5y + 9      
(iv) ax^1/2 + ax + 9x² + 4
(v) 3x² + 2x^-1 + 4x + 5
Solution:
(i) x² + 2x^-2 = x² + 2x \(\frac { 1 }{ { x }^{ 2 } }\) =x² + \(\frac { 1 }{ { x }^{ 2 } }\)
: It is not xx polynomial as it has negative integral power.
(ii) √ax + x² – x³: It is polynomial.
(iii) 3y³  √5y + 9 : It is a polynomial.
(iv) ax^1/2+ ax + 9x² + 4: It is not a polynomial as  the degree of \(\frac { 1 }{ { x }^{ 2 } }\) is an integer.
(v) 3x² + 2x^-1 + 4x + 5 : It is not a polynomial as the degree of x^–2, x^-1 are negative.

Question 3.
Write each of the following polynomials in the standard form. Also write their degree.
(i) x² + 3 + 6x + 5x⁴
(ii) a¹ + 4 + 5a⁶
(iii) (x³ – 1) (x³ – 4)
(iv) (y³ – 2) (y³ + 11)
(v) \(\left( { a }^{ 3 }-\frac { 3 }{ 8 } \right)\) \(\left( { a }^{ 3 }-\frac { 16 }{ 17 } \right)\)
(vi) \(\left( { a }+\frac { 3 }{ 4 } \right)\) \(\left( { a }+\frac { 3 }{ 4 } \right)\)
Solution:
Polynomial in standard form is the polynomial in ascending order or descending order.

Hope given RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.1 are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.7

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.7

Other Exercises

• RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.1
• RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.2
• RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.3
• RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.4
• RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.5
• RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.6
• RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.7
• RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.8
• RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.9

Factorize each of the following algebraic expressions :
Question 1.
x² + 12x – 45
Solution:

Question 2.
40 + 3x – x²
Solution:

Question 3.
a² + 3a-88
Solution:

Question 4.
a² – 14a – 51
Solution:

Question 5.
x² + 14x + 45
Solution:

Question 6.
x² – 22x + 120
Solution:

Question 7.
x²– 11x – 42
Solution:

Question 8.
a² + 2a – 3
Solution:

Question 9.
a² + 14a + 48
Solution:

Question 10.
x² – 4x – 21
Solution:

Question 11.
y² – 5y-36
Solution:

Question 12.
(a²-5a)²-36
Solution:

Question 13.
(a + 7) (a – 10) + 16
Solution:

Hope given RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.7 are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.8

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.8

Other Exercises

• RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.1
• RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.2
• RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.3
• RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.4
• RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.5
• RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.6
• RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.7
• RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.8
• RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.9

Resolve each of the following quadratic trinomials into factors :
Question 1.
2x² + 5x + 3
Solution:

Question 2.
2x²– 3x – 2
Solution:

Question 3.
3x² + 10x + 3
Solution:

Question 4.
7x – 6 – 2x²
Solution:

Question 5.
7x² – 19x – 6
Solution:

Question 6.
28-31x -5x²
Solution:

Question 7.
3 + 23y – 8y²
Solution:

Question 8.
11x² – 54x + 63
Solution:

Question 9.
7x-6x² + 20
Solution:

Question 10.
3x² + 22x + 35
Solution:

Question 11.
12x² – 17xy + 6y²
Solution:

Question 12.
6x² – 5xy – 6y²
Solution:

Question 13.
6x² + 13xy + 2y²
Solution:

Question 14.
14x² + 11xy – 15y²
Solution:

Question 15.
6a² + 17ab – 3b²
Solution:

Question 16.
36a² + 12abc – 15b²c²
Solution:

Question 17.
15x² – 16xyz – 15y²z²
Solution:

Question 18.
(x – 2y)² -5 (x- 2y) + 6
Solution:

Question 19.
(2a – b)² + 2 (2a – b) – 8
Solution:

Hope given RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.8 are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.