Question

Factorise each of the given : 64a³-27b³-144a²b+108ab²

Answer 1

Hello!

$\sf 64a^{3}- 27b^{3} - 144a^{2}b + 108ab^{2} \\ \\ \implies \sf 64a^{3} - 27b^{3}- 144a^{2}b + 108ab^{2} \\ \\ \implies \sf (4a)^{3}- (3b)^{3} - 3(4a)^{2}(3b) + 3(4a)(3b)^{2} \\ \\ \implies \sf (4a - 3b)^{3} \\ \\ \implies \boxed{\red{\bf{(4a - 3b)(4a - 3b)(4a - 3b)}}}$

Cheers!

Answer 2

Step-by-step explanation:

Hello!

\begin{gathered}\sf 64a^{3}- 27b^{3} - 144a^{2}b + 108ab^{2} \\ \\ \implies \sf 64a^{3} - 27b^{3}- 144a^{2}b + 108ab^{2} \\ \\ \implies \sf (4a)^{3}- (3b)^{3} - 3(4a)^{2}(3b) + 3(4a)(3b)^{2} \\ \\ \implies \sf (4a - 3b)^{3} \\ \\ \implies \boxed{\red{\bf{(4a - 3b)(4a - 3b)(4a - 3b)}}}\end{gathered}

64a

3

−27b

3

−144a

2

b+108ab

2

⟹64a

3

−27b

3

−144a

2

b+108ab

2

⟹(4a)

3

−(3b)

3

−3(4a)

2

(3b)+3(4a)(3b)

2

⟹(4a−3b)

3

⟹

(4a−3b)(4a−3b)(4a−3b)

Cheers!