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Question

Factorise : $${ 64a }^{ 2 }+96b+{ 36b }^{ 2 }$$


Solution

Given expression is $$64a^2+96b+36b^2$$

The expression can be written as:
$$(8a)^2+2(8)(6)b+(6b)^2$$
We know that, $$a^2+2ab+b^2=(a+b)^2$$
$$\therefore \ (8a)^2+2(8)(6)b+(6b)^2=(8a+6b)^2$$
$$\Rightarrow (8a+6b)(8a+6b)$$.

Hence, $$64a^2+96b+36b^2=(8a+6b)(8a+6b)$$.

Mathematics

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