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# Factoring this polynomial expression?

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The 1st line is the original expression:

and then i ended there because i wasn't sure what to do next.

firstly, am i correct so far? the tb answer is $${5(a+b)(13a+b)}$$

Jul 16, 2018

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The 1st line is the original expression:

In line three, there is a mistake:

The binom

$$(2a-b)^2 = (2a\cdot 2a -2ab-2ab+(-b)\cdot(-b) )\\=(4a^2-4ab+b^2)$$

The line four:

$$\begin{array}{|rcll|} \hline && 9(9a^2+6ab+b^2)-4(4a^2-4ab+b^2) \\ &=& 81a^2 +54ab+9b^2-16a^2+16ab-4b^2 \\ &=& 81a^2-16a^2 +54ab+16ab+9b^2-4b^2 \\ &=& 65a^2+70ab+5b^2 \\ &=& 5\cdot(13a^2+14ab+b^2) \\ &=& 5\cdot(a+b)(13a+b) \\ \hline \end{array}$$

Jul 16, 2018
edited by heureka  Jul 16, 2018