Question 178629


{{{-12x^2+147}}} Start with the given expression



{{{-3(4x^2-49)}}} Factor out the GCF {{{-3}}}



Now let's focus on the inner expression {{{4x^2-49}}}



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{{{4x^2-49}}} Start with the given expression.



{{{(2x)^2-49}}} Rewrite {{{4x^2}}} as {{{(2x)^2}}}.



{{{(2x)^2-(7)^2}}} Rewrite {{{49}}} as {{{(7)^2}}}.



Notice how we have a difference of squares {{{A^2-B^2}}} where in this case {{{A=2x}}} and {{{B=7}}}.



So let's use the difference of squares formula {{{A^2-B^2=(A+B)(A-B)}}} to factor the expression:



{{{A^2-B^2=(A+B)(A-B)}}} Start with the difference of squares formula.



{{{(2x)^2-(7)^2=(2x+7)(2x-7)}}} Plug in {{{A=2x}}} and {{{B=7}}}.



So this shows us that {{{4x^2-49}}} factors to {{{(2x+7)(2x-7)}}}.



In other words {{{4x^2-49=(2x+7)(2x-7)}}}.

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So {{{-3(4x^2-49)}}} then factors to {{{-3(2x+7)(2x-7)}}}



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Answer:


So {{{-12x^2+147}}} completely  factors to {{{-3(2x+7)(2x-7)}}}



In other words, {{{-12x^2+147=-3(2x+7)(2x-7)}}}