Factorize the following polynomial: x 2 + y + z 3 3 + x 3 - 2 y 3 + z 3 - 5 x 6 + y 3 + 4 z 3 3

Given: x 2 + y + z 3 3 + x 3 - 2 y 3 + z 3 - 5 x 6 + y 3 + 4 z 3 3 Use the algebraic identity a 3 + b 3 + c 3 - 3 abc = a + b + c a 2 + b 2 + c 2 - ab - bc - ca If a + b + c = 0 , then a 3 + b 3 + c 3 - 3 abc = 0 × a 2 + b 2 + c 2 - ab - bc - ca ⇒ a 3 + b 3 + c 3 = 3 abc a = x 2 + y + z 3 , b = x 3 - 2 y 3 + z , c = - 5 x 6 + y 3 + 4 z 3 Substitute the values in a 3 + b 3 + c 3 = 3 abc ⇒ 3 x 2 + y + z 3 × x 3 - 2 y 3 + z × - 5 x 6 + y 3 + 4 z 3 Therefore, the obtained solution is - 3 x 2 + y + z 3 x 3 - 2 y 3 + z 5 x 6 + y 3 + 4 z 3 .

E M B I B E

MATHEMATICS CLASS 9>Chapter 4 - Factorisation>EXERCISE-2.2>Q C

MEDIUM

9th West Bengal Board

IMPORTANT

Earn 100

Factorize the following polynomial: $x^{3} - 8 y^{3} + 64 z^{3} + 24 xyz$

Important Questions on Factorisation

MEDIUM

9th West Bengal Board

IMPORTANT

MATHEMATICS CLASS 9>Chapter 4 - Factorisation>EXERCISE-2.2>Q C

Factorize the following polynomial: ${(x - y)}^{3} + {(y - z)}^{3} + {(z - x)}^{3}$

MEDIUM

9th West Bengal Board

IMPORTANT

MATHEMATICS CLASS 9>Chapter 4 - Factorisation>EXERCISE-2.2>Q C

Factorize the following polynomial: ${(2 a - 3 b)}^{3} + {(4 c - 2 a)}^{3} + {(3 b - 4 c)}^{3}$ .

MEDIUM

9th West Bengal Board

IMPORTANT

MATHEMATICS CLASS 9>Chapter 4 - Factorisation>EXERCISE-2.2>Q C

Factorize the following polynomial: ${(\frac{x}{2} + y + \frac{z}{3})}^{3} + {(\frac{x}{3} - \frac{2 y}{3} + z)}^{3} - {(\frac{5 x}{6} + \frac{y}{3} + \frac{4 z}{3})}^{3}$