Question

Factorrise : p2 + 10p + 25.​

Answer 1

Answer : (p + 5) (p + 5)

Step by step Explanation:

Given equation : $p^2 + 10p + 25$

On Comparing the given equation from $\sf \rm ax^2 + bx + c$,

We get,

b = 10

c = 25

Sum, = 10

product = 25

Numbers are = 5, 5

As, 5 + 5 = 10 and 5 x 5 = 25

So,

$\rm \therefore p^2 + 10p + 25 \\ \rm \implies p \times p + 5p + 5p + 5 \times 5 \\ \rm \implies p(p + 5) + 5(p + 5) \\ \rm \implies \bf (p+5)(p+5)$

Alternative method:

Using Identity $(a+b)^2 = a^2 + 2ab + b^2$, We can factorise the given equation,

$\therefore \rm p^2 + 10p + 25 \\ \implies \rm (p)^2 + 2(p)(5) + (5)^2$

On comparing the given equation by the the identity, We get

a = p

b = 5

So,

$\rm \therefore (p)^2 + 2(p)(5) + (5)^2 \\ \rm \implies (p+5)^2 \\ \rm \implies \bf (p+5) (p+5)$

Answer 2

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p2 – 10p + 25

Here, 5 + 5 = 10 and 5 × 5 = 25

p2 – 10p + 25

= p2 – 5p – 5p + 5 × 5

= (p2 – 5p) + (-5p + 25)

= p(p – 5) – 5(p – 5)

= (p – 5) (p – 5)

= (p – 5)2