What is factor (p+q)^2+10(p+q)+25 ?

The solution to factor (p+q)^2+10(p+q)+25 is (p+q+5)^2

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factor (p+q)^2+10(p+q)+25

factor

(p + q)^{2} + 10 (p + q) + 25

(p + q + 5)^{2}

Solution steps

(p + q)^{2} + 10 (p + q) + 25

Rewrite

(p + q)^{2} + 10 (p + q) + 25

(p + q)^{2} + 2 (p + q) \cdot 5 + 5^{2}

= (p + q)^{2} + 2 (p + q) \cdot 5 + 5^{2}

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

a = (p + q), b = 5

= ((p + q) + 5)^{2}

Refine

= (p + q + 5)^{2}

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What is factor (p+q)^2+10(p+q)+25 ?
The solution to factor (p+q)^2+10(p+q)+25 is (p+q+5)^2