Question

Factories A CUBE Plus 64​

Answer 1

$\bf{\large{\underline{\underline{Answer:-}}}}$

a³ + 64 = (a + 4)(a² - 4a + 16)

$\bf{\large{\underline{\underline{Explanation:-}}}}$

a³ + 64

This can be written as :

= (a)³ + (4)³

[Since 64 can be written as cube of 4 So, (4)³ = 64]

We know that, x³ + y³ = (x + y)(x² - xy + y²)

Here, x = a and y = 4

By substituting the values in the identity we have,

= {a + 4}{(a)² - a(4) + (4)²}

= (a + 4)(a² - 4a + 16)

So a³ + 64 = (a + 4)(a² - 4a + 16)

$\bf{\large{\underline{\underline{Identity\:Used:-}}}}$

x³ + y³ = (x + y)(x² - xy + y²)

$\bf{\large{\underline{\underline{Extra\:Info:-}}}}$

What is factorisation?

Factorization is a process of writing the given expression as a product of its factors.

1) Factorisation by grouping terms

Example :-

ax + bx + ay + by = x(a + b) + y(a + b)

= (a + b)(x + y)

2) Factorisation using identities :-

Example :-

25p² - 16q² = (5p)² - (4q)²

= (5p + 4q)(5p - 4q)

$\bf{\large{\underline{\underline{Important\:Identities:-}}}}$

[1] (x + y)² = x² + y² + 2xy

[2] (x - y)² = x² + y² - 2xy

[3] (x + a)(x + b) = x² + (a + b)x + ab

$\bf{\underline{\underline{Note:-}}}$

You should be perfect with algebraic identities to do factorization.