Factorise- x 2-10 x -25A- x-5x-5B- x-52C- x-52D- x-5x-2

The correct option is B The expression x^2 + 10x + 25 can be written as, =x^2 +2 × 5 × x +5^2...(i) Comparing (i) with the identity (a + b)^2 = a^2 + 2ab + b^ ...

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Byju's Answer

Standard VII

Mathematics

Factorisation of Algebraic Expressions Using Identities

Factorise: x ...

Question

Factorise: $x^{2} + 10 x + 25$

(x + 5)(x - 5)

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(x + 5)(x + 2)

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Solution

The correct option is B

The expression $x^{2} + 10 x + 25$ can be written as,

$= x^{2} + 2 \times 5 \times x + 5^{2}$ ...(i)

Comparing (i) with the identity $(a + b)^{2} = a^{2} + 2 a b + b^{2}$ , we get
$a^{2} = x^{2} \Rightarrow a = x$

$b^{2} = 5^{2} \Rightarrow b = 5$

$\Rightarrow$ $x^{2} + 10 x + 25$ = $x^{2} + 2 (x) (5) + 5^{2}$ = $(x + 5)^{2}$
Therefore, the factors of $x^{2} + 10 x + 25$ are $(x + 5)$ and $(x + 5)$ .

Suggest Corrections

Factorise: x2+10x+25

The correct option is B The expression x2+10x+25 can be written as, =x2+2×5×x+52...(i) Comparing (i) with the identity (a+b)2=a2+2ab+b2, we get a2=x2⇒a=x b2=52⇒b=5 ⇒ x2+10x+25=x2+2(x)(5)+52 = (x+5)2 Therefore, the factors of x2+10x+25​​​​​​​ are (x+5) and (x+5).

Factorise: $x^{2} + 10 x + 25$