Question

factorize (a²-4a)(a²-4a-1)-20

Answer 1

The factorisation of $(a^2-4a)(a^2-4a-1)-20$ is equal to$a(a-4)[(a+1)(a-1)-4a]-20$.

Step-by-step explanation:

We have,

$(a^2-4a)(a^2-4a-1)-20$

To find, the factorisation of $(a^2-4a)(a^2-4a-1)-20$ = ?

∴ $(a^2-4a)(a^2-4a-1)-20$

$=(a^2-4a)(a^2-1-4a)-20$

$=a(a-4)(a^2-1^2-4a)-20$

$=a(a-4)[(a+1)(a-1)-4a]-20$

Using the algebraic identity,

$x^{2} -y^{2} =(x+y)(x-y)$

$=a(a-4)[(a+1)(a-1)-4a]-20$

∴ The factorisation of $(a^2-4a)(a^2-4a-1)-20$ $=a(a-4)[(a+1)(a-1)-4a]-20$

Thus, the factorisation of $(a^2-4a)(a^2-4a-1)-20$ is equal to$a(a-4)[(a+1)(a-1)-4a]-20$.