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Mathematics 17 Online
OpenStudy (calculusxy):

factoring quadratic expression...

OpenStudy (calculusxy):

\[\huge 294a^2 - 54 \]

OpenStudy (calculusxy):

@Nnesha

OpenStudy (calculusxy):

@jim_thompson5910 @hartnn @Jhannybean

OpenStudy (calculusxy):

\[\large 294a^2 - 0a - 54\]

OpenStudy (anonymous):

larget common factor of \(294\) and \(24\) is?

OpenStudy (anonymous):

get rid of that stupid zero

OpenStudy (calculusxy):

okay sorry

OpenStudy (calculusxy):

don't you mean the gcf of 294 and 54 ?

OpenStudy (anonymous):

yes i get 6

OpenStudy (jhannybean):

Hahahaha

OpenStudy (anonymous):

so start with \[6(49a^2-9)\] then factor \[49a^2-9\] as the difference of two squares

OpenStudy (jhannybean):

\[a^2-b^2 = (a-b)(a+b)\]

OpenStudy (calculusxy):

(7a + 3)(7a - 3)

OpenStudy (jhannybean):

or rather,.... \(ca^2-b^2 = (ca-b)(ca+b)\) :') \(c\) is the coefficient of one of the terms lol

OpenStudy (anonymous):

\[\heartsuit^2-\spadesuit^2=(\heartsuit+\spadesuit)(\heartsuit -\spadesuit)\][

OpenStudy (jhannybean):

Oh you think you're fancy huh

OpenStudy (anonymous):

just showing off

OpenStudy (jhannybean):

lol

OpenStudy (anonymous):

\[\xi^2 -\omega^2=(\xi+\omega)(\xi-\omega)\]

OpenStudy (jhannybean):

You are correct @calculusxy , just don't forget to multiply by the 6

OpenStudy (calculusxy):

can i make sure the answer to another question?

OpenStudy (calculusxy):

\[\large 12x^2 + 12x + 3\] \[\huge Answer \] \[\large 3(2x+1)(2x+1)\]

OpenStudy (anonymous):

looks good to me you @Jhannybean ?

OpenStudy (calculusxy):

well i did the same question, but in a different way and got a different answer ( can u catch my mistake) 12x^2 + 12x + 3 12x^2 + 6x + 6x + 3 2x(2x+3) 3(2x + 3) (2x - 3)(2x + 3)

OpenStudy (jhannybean):

\[\begin{align}12x^2+12x+3 &\rightarrow 4x^2+4x+1 \\&\rightarrow x^2+4x+4 \\&\rightarrow (x+2)(x+2) \\&\rightarrow \left(x+\frac{2}{4}\right)\left(x+\frac{2}{4}\right) \\&\rightarrow \left(x+\frac{1}{2}\right)\left(x+\frac{1}{2}\right) \\&\rightarrow \color{red}{(2x+1)(2x+1)}\end{align} \]

OpenStudy (jhannybean):

For this method i simplify the quadratic by putting it in standard form \(ax^2+bx+c\) typically where \(a=1\) find the factors divide the factors by the leading coefficient we used to simplify our equation If the simplification of the factors does not give you an integer value but a fractional one, multiply the variable with the denominator of the fraction. You'll have your factorization

Nnesha (nnesha):

if there is a GCF better to take it out |dw:1444172023392:dw|

Nnesha (nnesha):

|dw:1444172039740:dw|

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