Question

8l³-36l²m+54lm²-27m³​

Answer 1

ANSWER:

To Factorise:

• 8l³ - 36l²m + 54lm² - 27m³

Solution:

We are given that,

$\implies 8l^3-36l^2m+54lm^2-27m^3$

We can re write it as,

$\implies (2\times2\times2)l^3-(3\times2\times2\times3)l^2m+(3\times2\times3\times3)lm^2-(3\times3\times3)m^3$

So,

$\implies 2^3l^3-3(2^2l^2)(3m)+3(2l)(3^2m^2)-3^3m^3$

We know that,

$\hookrightarrow a^xb^x=(ab)^x$

So,

$\implies 2^3l^3-3(2^2l^2)(3m)+3(2l)(3^2m^2)-3^3m^3$

$\implies (2l)^3-3(2l)^2(3m)+3(2l)(3m)^2-(3m)^3$

We know that,

$\hookrightarrow (x-y)^3=x^3-3x^2y+3xy^2-y^3$

Here, x = 2l and y = 3m. So,

$\implies (2l)^3-3(2l)^2(3m)+3(2l)(3m)^2-(3m)^3$

$\implies \bf (2l-3m)^3$

Therefore,

$\implies\bf 8l^3-36l^2m+54lm^2-27m^3= (2l-3m)^3$