Question

$a {}^{2} + 8a + 16$
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Answer 1

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• Factorise :-

${a}^{2} + 8a + 16$

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✯ We can easily factorise this equation by using suitable algebraic identity. Here, the applicable identity is –

$\boxed{ \orange{ (a+b)²=a²+2ab+c²}}$

Using the above identity, let's factorise, i.e -

${a}^{2} + 8a + 16 \\ \implies \: (a) {}^{2} + 2(a \times4) + (4) {}^{2} \\ \\ \implies\boxed{ \bold{(a + 4) {}^{2} }}$

∴ After factorisation, a²+8a+16 = (a+4)²

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✍️More to know :

♦ The algebraic equations which are valid for all values of variables in them are called algebraic identities.

♦ Some of the algebraic identities are–

• $\boxed{(a + b) {}^{2} = {a}^{2} + 2ab + {b}^{2} }$

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• $\boxed{(a - b) {}^{2} = {a}^{2} - 2ab + {b}^{2} }$

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• $\boxed{ {a}^{2} - {b}^{2} = (a + b)(a - b)}$

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• $\boxed{(x+a)(x+b)={x}^{2}+(a + b)x+ab}$

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• $\boxed{(a + b){}^{3}={a}^{3}+b{}^{3} +3ab(a+b)}$

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