Question

factor each of the following expressions.
a. ( x^{2}+10 x + 25=)
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b. ( x^{2}+40 x + 400=)
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Explanation:

Step1: Recall the perfect - square formula

The perfect - square formula is \(a^{2}+2ab + b^{2}=(a + b)^{2}\).

Step2: Factor \(x^{2}+10x + 25\)

For the expression \(x^{2}+10x + 25\), we have \(a=x\), \(2ab = 10x\). If \(a=x\), then \(2b=10\), so \(b = 5\). And \(b^{2}=25\).
Using the formula \(a^{2}+2ab + b^{2}=(a + b)^{2}\), we get \(x^{2}+10x + 25=(x + 5)^{2}\).

Step3: Factor \(x^{2}+40x + 400\)

For the expression \(x^{2}+40x + 400\), we have \(a=x\), \(2ab=40x\). If \(a = x\), then \(2b=40\), so \(b = 20\). And \(b^{2}=400\).
Using the formula \(a^{2}+2ab + b^{2}=(a + b)^{2}\), we get \(x^{2}+40x + 400=(x + 20)^{2}\).

Answer:

a. \((x + 5)^{2}\)
b. \((x + 20)^{2}\)