## 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.**

**4x**

^{2}+ 12xy + 9y^{2 }**Solution:**

4x

^{2}+ 12xy + 9y

^{2}= (2x)

^{2}+ 2 x 2x x 3y + (3y)

^{2}{∵ a

^{2}+ 2ab + b

^{2}= (a +b)

^{2}}

^{ }= (2x + 3y)

^{2 }

**Question 2.
**

**9a**

^{2}– 24ab + 16b^{2 }**Solution:**

9a

^{2}– 24ab + 16b

^{2 }= (3a)

^{2}– 2 x 3a x 4b + (4b)

^{2 }{∵ a

^{2}– 2ab + b

^{2}= (a – b)

^{2}}

= (3a – 4b)

^{2}

**Question 3.
**

**36a**

^{2}– 6pqr + 9r^{2 }

**Solution:**

p

^{2}q

^{2}– 6pqr + 9r

^{2}

= (pq)

^{2}– 2 x pq x3r + (3r)

^{2 }{∵ a

^{2}– 2ab + b

^{2}= (a -b)

^{2}}

= (pq-3r)

^{2}

**Question 4.
**

**36a**

^{2}+ 36a + 9**Solution:**

36a

^{2}+ 36a + 9

= (6a)

^{2}+ 2 x 6a x 3 + (3)

^{2 }{∵ a

^{2}+ 2ab + b

^{2}= (a + b)

^{2 }= (6a + 3)

^{2}

**Question 5.
**

**a**

^{2}+ 2ab + b^{2}– 16**Solution:**

a

^{2}+ 2ab + b

^{2}– 16

= (a + b)

^{2}– (4)

^{2}{∵ a

^{2}+ 2ab + b

^{2}= (a + b)

^{2}and a

^{2}– b

^{2}= (a + b) (a – b)}

= (a + b + 4) (a + b – 4)

**Question 6.
**

**9z**

^{2}– x^{2}+ 4xy – 4y^{2 }

**Solution:**

9z

^{2}– x

^{2}+ 4xy – 4y

^{2 }{∵ a

^{2}– b

^{2}= (a + b) (a – b) and a

^{2}– 2ab + b

^{2 }(a – b)

^{2}}

= 9z

^{2}– (x

^{2}– 4xy + 4y

^{2})

= (3z)

^{2}– [(x)

^{2}– 2 x x x 2y + (2y)

^{2}]

= (3z)

^{2}-(x-2y)

^{2 }= (3z + x – 2y) (3z – x + 2y)

**Question 7.
**

**9a**

^{4}– 24a^{2}b^{2}+ 16b^{4}– 256**Solution:**

**Question 8.
**

**16 – a**

^{6}+ 4a^{3}b^{3}– 4b^{6 }

**Solution:**

**Question 9.
**

**a**

^{2}– 2ab + b^{2}– c^{2 }

**Solution:**

**Question 10.
**

**x**

^{2}+ 2x + 1 – 9y^{2 }**Solution:**

**Question 11.
**

**a**

^{2}+ 4ab + 3b^{2 }

**Solution:**

a

^{2}+ 4ab + 3b

^{2}

= a

^{2}+ 4ab+ 4b

^{2}– b

^{2 }= (a)

^{2}+ 2 x a x 2b + (2b)

^{2}– b

^{2 }(∵ 3b

^{2}= 4b

^{2}– b

^{2})

= (a + 2b)

^{2}– (b)

^{2 }{∵ a

^{2}– b

^{2}= (a +b) (a – b)}

= (a + 2b + b) (a + 2b- b)

**Question 12.
**

**96 – 4x-x**

^{2 }**Solution:**

96 – 4x – x

^{2}= 96 – (4x + x

^{2})

= 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.
**

**a**

^{4}+ 3a^{2}+ 4**Solution:**

a

^{4}+ 3a

^{2}+ 4

= (a

^{2})

^{2}+ (2)

^{2}+ 2 x a

^{2}x 2 – a

^{2 }(on completing the square)

= (a

^{2}+ 2)

^{2}– (a)

^{2 }= (a

^{2}+ 2 + a) (a

^{2}+ 2 – a)

= (a

^{1}+ a + 2) (a

^{2}– a + 2)

**Question 14.
**

**4a**

^{4}+ 1**Solution:**

4x

^{4}+ 1 = (2a

^{2})

^{2}+ (1)

^{2}+ 2 x 2x

^{2}x 1 – 2 x 2x

^{2 }x 1 (completing the square)

= (2x

^{2}+ 1)

^{2}– 4a

^{2}

= (2x

^{2}+ 1)

^{2}– (2a)

^{2 }{a

^{2}– b

^{2}= (a + b) (a – b)}

= (2x

^{2}+ 1 + 2a) (2a

^{2}+ 1 – 2a)

= (2a

^{2}+ 2a + 1) (2a

^{2}– 2a + 1)

**Question 15.
**

**4x**

^{4}+y^{4 }**Solution:**

4a

^{4}+ y

^{4}= (2x

^{2})

^{2}+ (y

^{2})

^{2}+ 2 x 2x

^{2}y

^{2}– 2 x 2x

^{2}y

^{2 }= (2x

^{2}+ y

^{2})

^{2}– 4x

^{2}y

^{2}

= (2x

^{2}+ y

^{2})

^{2}– (2xy)

^{2 }= (2x

^{2}+ y

^{2}+ 2xy) (2x

^{2}+ y

^{2}– 2xy)

= (2x

^{2}+ 2xy + y

^{2}) (2x

^{2}– 2xy + y

^{2})

**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 –*p^{2}– q^{2}– 2pq**Solution:**

**Question 18.
**

**a**

^{2}+ 9y^{2}– 6xy – 25a^{2 }

**Solution:**

**a**

^{2}+ 9y^{2}– 6xy – 25a^{2 }

**Question 19.
**

**49 – a**

^{2}+ 8ab – 16b^{2 }

**Solution:**

**Question 20.
**

**a**

^{2}– 8ab + 16b^{2}– 25c^{2 }

**Solution:**

**Question 21.
**

**x**

^{2}-y^{2}+ 6y- 9**Solution:**

**Question 22.
**

**25x**

^{2}– 10x + 1 – 36y^{2 }**Solution:**

**Question 23.
**

**a**

^{2}-b^{2}+*2*bc – c^{2 }

**Solution:**

**Question 24.
**

**a**

^{2}+ 2ab + b^{2}-c^{2 }

**Solution:**

**Question 25.
**

*49*-x^{2}– y^{2}+ 2xy**Solution:**

**Question 26.
**

**a**

^{2}*+**4*b^{2}–*4*ab*–*4c^{2 }

**Solution:**

**Question 27.
**

**x**

^{2}-y^{2}*–*4xz + 4z^{2 }

**Solution:**

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

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