Question

Factorise :-
x² + 8x + 16​

Answer 1

Answer:

(x+4)^2

Step-by-step explanation:

x^2+8x+16=x^2+2×4×x+4^2

=(x+4)^2

since,(a+b)^2=a^2+2ab+b^2

(or)

x^2+8x+16=x^2+4x+4x+16

=x(x+4)+4(x+4)

=(x+4)(x+4)

=(x+4)^2

hope it helped u

Answer 2

Given Equation:-

• x² + 8x + 16

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To find:-

• Value of x.

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Solution:-

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{\tt{\bigstar{Concept{\bigstar}}}}$

Observe the expression; it has three terms. Therefore, it does not fit Identity III. Also, it's first and third terms are perfect squares with a positive sign before the middle term. So, it is of the form a² + 2ab + b² where a = x and b = 4.

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Such that,

$\tt\longrightarrow\: \: \: \: \: \:\: \: \: \: \: \:\: \: \: \: \: \:\: \: \: \: \: \:\: \: \: \: \: \:{a^2 + 2ab + b^2}$

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$\tt\longrightarrow\: \: \: \: \: \:\: \: \: \: \: \:\: \: \: \: \: \:{x^2 + 2 (x) (4) + 4^2}$

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$\tt\longrightarrow\: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \:{x^2 + 8x + 16}$

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Since,

$\tt\longrightarrow\: \: \: \: \: \: \: \: \: \: \: \:{a^2 + 2ab + b^2}$

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$\tt\longrightarrow\: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \:{(a + b)^2}$

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By comparison,

$\tt\longrightarrow\: \: \: \: \: \: \: \: \: \: \: \:{x^2 + 8x + 16}$

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$\tt\longrightarrow\: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \:{\boxed{\red{(x + 4)^2}}}$