Question

Factorise the following:
i) 27x3 - 27 x2y + 9xy2 - y3
ii ) 4x2 + 9y2 + 16z2+ 12xy - 24yz - 8xz.

Answer 1

Answer:

I) 27x3 - 27x2y + 9xy2 - y3

ii) (2×+3y-4z) (2×+3y-4z)

Answer 2

ANSWER:

To Factorize:

• 27x^3 - 27x^2y + 9xy^2 - y^3
• 4x^2 + 9y^2 + 16z^2 + 12xy - 24yz - 8xz

Solution:

1. 27x^3 - 27x^2y + 9xy^2 - y^3

We are given that,

$\implies 27x^3 - 27x^2y + 9xy^2 - y^3$

$\implies 3^3x^3 - 3\times3^2x^2y + 3\times3xy^2 - y^3$

$\implies (3x)^3 - 3(3x)^2y + 3(3x)(y)^2 - (y)^3$

We know that,

$\hookrightarrow a^3-3a^2b+3ab^2-b^3=(a-b)^3$

So,

$\implies (3x)^3 - 3(3x)^2y + 3(3x)(y)^2 - (y)^3$

$\implies (3x-y)^3$

Hence,

$\implies\bf 27x^3 - 27x^2y + 9xy^2 - y^3= (3x-y)^3$

2. 4x^2 + 9y^2 + 16z^2 + 12xy - 24yz - 8xz

We are given that,

$\implies 4x^2 + 9y^2 + 16z^2 + 12xy - 24yz - 8xz$

$\implies 2^2x^2 + 3^2y^2 + 4^2z^2 + 2(2x)(3y) - 2(3y)(4z) - 2(2x)(4z)$

$\implies (2x)^2 + (3y)^2 + (-4z)^2 + 2(2x)(3y) + 2(3y)(-4z) + 2(2x)(-4z)$

We know that,

$\hookrightarrow a^2+b^2+c^2+2ab+2bc+2ca=(a+b+c)^2$

So,

$\implies (2x)^2 + (3y)^2 + (-4z)^2 + 2(2x)(3y) + 2(3y)(-4z) + 2(2x)(-4z)$

$\implies (2x+3y-4z)^2$

Hence,

$\implies\bf 4x^2 + 9y^2 + 16z^2 + 12xy - 24yz - 8xz = (2x+3y-4z)^2$