Question

factorise 84-2r-2r^2

Answer 1

$84 - 2r - 2 {r}^{2} \\ = 2( - {r}^{2} - r + 42) \\ = - 2( {r}^{2} + 7r - 6r - 42) \\ = - 2r(r + 7) + 12(r + 7) \\ =\bold{\purple{2(6 - r)(r + 7)}}$
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Answer 2

$84-2r-2r^2 = -2\left(r-6\right)\left(r+7\right)$

Solution:

Given, we have to factorize the following:

$84 - 2r - 2r^2$

We have to write as a product of factors

From given,

$84 - 2r - 2r^2\\\\\mathrm{Factor\:out\:common\:term\:}-2\\\\-2\left(r^2+r-42\right) \\\\\mathrm{Factor}\:r^2+r-42: \\\\Split\ the\ middle\ term\\\\-2(r^2 -6r+7r - 42) \\\\\mathrm{Break\:the\:expression\:into\:groups}$

$-2(\left(r^2-6r\right)+\left(7r-42\right))\\\\\mathrm{Factor\:out\:}r\mathrm{\:from\:}r^2-6r\mathrm{:\quad }\\\\\mathrm{Factor\:out\:}7\mathrm{\:from\:}7r-42\mathrm{:\quad }\\\\-2(r\left(r-6\right)+7\left(r-6\right))\\\\\mathrm{Factor\:out\:common\:term\:}r-6\\\\-2\left(r-6\right)\left(r+7\right)$

Thus the factored expression is:

$84-2r-2r^2 = -2\left(r-6\right)\left(r+7\right)$

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