## RD Sharma Class 9 Solutions Chapter 5 Factorisation of Algebraic Expressions Ex 5.3

These Solutions are part of RD Sharma Class 9 Solutions. Here we have given RD Sharma Class 9 Solutions Chapter 5 Factorisation of Algebraic Expressions Ex 5.3

Other Exercises

- RD Sharma Class 9 Solutions Chapter 5 Factorisation of Algebraic Expressions Ex 5.1
- RD Sharma Class 9 Solutions Chapter 5 Factorisation of Algebraic Expressions Ex 5.2
- RD Sharma Class 9 Solutions Chapter 5 Factorisation of Algebraic Expressions Ex 5.3
- RD Sharma Class 9 Solutions Chapter 5 Factorisation of Algebraic Expressions Ex 5.4
- RD Sharma Class 9 Solutions Chapter 5 Factorisation of Algebraic Expressions VSAQS
- RD Sharma Class 9 Solutions Chapter 5 Factorisation of Algebraic Expressions MCQS

Factorize:

Question 1.

64a^{3} + 125b^{3} + 240a^{2}b + 300ab^{2
}Solution:

64a^{3} + 125b^{3} + 240a^{2}b + 300ab^{2
}= (4a)^{3} + (5b)^{3} + 3 x (4a)^{2} x 5b + 3(4a) + (5b)^{2
}= (4a + 5b)^{3}

= (4a + 5b) (4a + 5b) (4a + 5b)

Question 2.

125x^{3} – 27y^{3} – 225x^{2}y + 135xy^{2
}Solution:

125x^{3} – 27y^{3} – 225x^{2}y + 135xy^{2
}= (5x)^{3} – (3y)^{3} – 3 x (5x)^{2} x (3y) + 3- x 5x x (3y)^{2
}= (5x –* 3y) ^{3}
= *(5x

*– 3*y) (5x –

*3*y) (5x –

*3y)*

Question 3.

Solution:

Question 4.

8x^{3} + 27y^{3} + 36x^{2}y + 54xy^{2
}Solution:

8x^{3} + 27y^{3} + 16x^{2}y + 54xy^{2
}= (2x)^{3} + (3y)^{3} + 3 x (2x)^{2} x 3y + 3 x 2x x (3y)^{2
}= (2x + 3y)^{3}

= (2x + 3y) (2x + 3y) (2x + 3y)

Question 5.

a^{3} – 3a^{2}b + 3ab^{2} – b^{3} + 8

Solution:

a^{3} – 3a^{2}b + 3ab^{2} – b^{3} + 8

= (a – b)^{3} + (2)^{3
}= (a – b + 2) [(a -b)^{2}– (a – b) x 2 + (2)^{2}]

= (a- b + 2) (a^{2} + b^{2} -2ab – 2a + 2b + 4)

Question 6.

x^{3} + 8y^{3} + 6x^{2}y + 12xy^{2
}Solution:

x^{3} + 8y^{3} + 6x^{2}y + 12xy^{2}

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

= (x + 2y) (x + 2y) (x + 2y)

Question 7.

8x^{3} + y^{3} + 12x^{2}y + 6xy^{2
}Solution:

8x^{3} + y^{3} + 12x^{2}y + 6xy^{2
}= (2x)^{3} + (y)^{3} + 3 x (2x)^{2} x y + 3 x 2x x y^{2}

= (2x + y)^{3}

= (2x + y) (2x + y) (2x + y)

Question 8.

8a^{3} + 27b^{3} + 36a^{2}b + 54ab^{2 }

Solution:

8a^{3} + 27b^{3} + 16a^{2}b + 54ab^{2
}= (2a)^{3} + (3b)^{3} + 3 x (2a)^{2 }x 3b + 3 x 2a x (3b)^{2
}= (2a + 3b)^{3}

= (2a + 3b) (2a + 3b) (2a + 3b)

Question 9.

8a^{3} – 27b^{3} – 36a^{2}b + 54ab^{2 }

Solution:

8a^{3} – 27b^{3} – 36a^{2}b + 54ab^{2
}= (2a)^{3} – (3b)^{3} – 3 x (2a)^{2} x 3b + 3 x 2a x (3b)^{2
}= (2a – 3b))^{3}

= (2a – 3b) (2a – 3b) (2a – 3b)

Question 10.

x^{3} – 12x(x – 4) – 64

Solution:

x^{3} – 12x(x – 4) – 64

= x^{3} – 12x^{2} + 48x – 64

= (x)^{3} – 3 x x^{2} x 4 + 3 x x x (4)^{2}– (4)^{3
}= (x – 4)^{3}

= (x – 4) (x – 4) (x – 4)

Question 11.

a^{3}x^{3} – 3a^{2}bx^{2} + 3ab^{2}x – b^{3 }

Solution:

a^{3}x^{3} – 3a^{2}bx^{2} + 3ab^{2}x – b^{3
}= (ax)^{3} – 3 x (ax)^{2} x b + 3 x ax x (b)^{2}– (b)^{3
}= (ax – b)^{3}

= (ax – b) (ax – b) (ax – b)

Hope given RD Sharma Class 9 Solutions Chapter 5 Factorisation of Algebraic Expressions Ex 5.3 are helpful to complete your math homework.

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