Question

factor each of the following expressions
a $16x^{2}-40x + 25=$
b $36x^{2}+24x + 4=$
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Explanation:

Step1: Recall the perfect - square formula

The perfect - square formula is \((a\pm b)^2=a^{2}\pm2ab + b^{2}\).

Step2: Factor \(16x^{2}-40x + 25\)

For \(16x^{2}-40x + 25\), we have \(a = 4x\) (since \((4x)^{2}=16x^{2}\)), \(b = 5\) (since \(5^{2}=25\)), and \(2ab=2\times4x\times5 = 40x\).
So, \(16x^{2}-40x + 25=(4x - 5)^{2}\).

Step3: Factor \(36x^{2}+24x + 4\)

For \(36x^{2}+24x + 4\), we have \(a = 6x\) (since \((6x)^{2}=36x^{2}\)), \(b = 2\) (since \(2^{2}=4\)), and \(2ab=2\times6x\times2=24x\).
So, \(36x^{2}+24x + 4=(6x + 2)^{2}=4(3x + 1)^{2}\).

Answer:

a. \((4x - 5)^{2}\)
b. \(4(3x + 1)^{2}\)