How do you factor : 48x^2+72x+27?

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How do you factor : 48x^2+72x+27?

I know the GCF which is 3 but I am not sure how to use the perfect square patterns on this problem after I have found the GCF?

2 Answers

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Answer 1 · 2018-03-01T03:43:42

$3 {(4 x + 3)}^{2}$ $3(4x+3)^2$

Explanation:

$16 x^{2} + 24 x + 9$ $16x^2+24x+9$

$4^{2}$ $4^2$ is $16$ $16$ and $3^{2}$ $3^2$ is $9$ $9$

$(4 x + 3) (4 x + 3)$ $(4x+3)(4x+3)$

$4 x \cdot 4 x = 16 x^{2}$ $4x*4x = 16x^2$

$4 x \cdot 3 + 4 x \cdot 3 = 12 x + 12 x = 24 x$ $4x*3 + 4x*3 = 12x + 12x = 24x$

$3 \cdot 3 = 9$ $3*3 = 9$

$16 x^{2} + 24 x + 9 = {(4 x + 3)}^{2}$ $16x^2+24x+9 = (4x+3)^2$

$48 x^{2} + 72 x + 27 = 3 {(4 x + 3)}^{2}$ $48x^2+72x+27 = 3(4x+3)^2$

Answer 2 · 2018-03-01T03:56:42

$3 {(4 x + 3)}^{2}$ $3(4x + 3)^2$

Explanation:

Use the new AC method to factor trinomials (Socratic Search)
$y = 48 x^{2} + 72 x + 27 =$ $y = 48x^2 + 72x + 27 =$ 48(x + p)(x + q)
Converted trinomial:
$ý = x^2 + 72 x + 1296 = (x + 36)^2$ .
We have (p')= (q') = (36).
Therefor, $p = q = (p')/a = 36/48 = 3/4$
Factored form:
$y = 48(x + 3/4)^2 = 3(4x + 3)^2$

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How do you factor : 48x^2+72x+27?

I know the GCF which is 3 but I am not sure how to use the perfect square patterns on this problem after I have found the GCF?

2 Answers

Explanation:

Explanation:

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