How do you factor $4 x^{2} + 9 + 12 x$ $4x^2+9+12x$ using the perfect squares formula?

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How do you factor $4 x^{2} + 9 + 12 x$ $4x^2+9+12x$ using the perfect squares formula?

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Answer 1 · 2017-05-31T11:40:58

${(2 x + 3)}^{2}$ $(2x+3)^2$

Explanation:

The perfect squares formula says that $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ $a^2+2ab+b^2=(a+b)^2$
You can see $4 x^{2} + 9 + 12 x$ $4x^2+9+12x$ as $2^{2} x^{2} + 3^{2} + (3 \cdot 2) x = {(2 x)}^{2} + (3 \cdot 2) x + 3^{2}$ $2^2x^2+3^2+(3*2)x=(2x)^2+(3*2)x+3^2$
In this case you have $a = 2 x$ $a=2x$ , $b = 3$ $b=3$ and $2 a b = 2 (2 x \cdot 3) = (2 \cdot 2 \cdot 3) x = 12 x$ $2ab=2(2x*3)=(2*2*3)x=12x$

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How do you factor $4 x^{2} + 9 + 12 x$ $4x^2+9+12x$ using the perfect squares formula?

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How do you factor $4 x^{2} + 9 + 12 x$ $4x^2+9+12x$ using the perfect squares formula?