Question

Factorise the following

1. 8a cube+64b cube

2. 125m cube -343n cube

Answer 1

1) 8a^3+64b^3
=(2a)^3+(4b)^3
=(2a+4b)(4a^2-8ab+16b^2)

2)125m^3-343n^3
=(5m)^3-(7n)^3
=(5m-7n)(25m^2+35mn+49n^2)

Answer 2

♦8a³+64b³
=(2a)³+(4b³
a³+b³= (a+b)(a2-ab+b2)
(2a)³+(4b)³=(2a+4b)[(2a)²-(2a)(4b)+(4b)²]
=(2a+4b)(4a²-8ab+16b²)

♦125m³-343n³
=(5m)³-(7n)³
a³-b³=(a-b)(a²+ab+b²)
(5m)³-(7n)³=(5m+7n)[(5m)²+(5m)(7n)+(7n)²]
=(5m+7n)(25m²+35m+48n²)

Hope it helps