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Multiplication of Two Binomials

If 3x-45x+7 =...

Question

If $(3 x - 4) (5 x + 7) = 15 x^{2} - a x - 28$ , then $a$ is ______.

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Solution

$(3 x - 4) (5 x + 7) = 15 x^{2} - a x - 28$

$\Rightarrow$ $15 x^{2} + 21 x - 20 x - 28 = 15 x^{2} - a x - 28$
$\Rightarrow$ $15 x^{2} + x - 28 = 15 x^{2} - a x - 28$
$\Rightarrow$ $x = - a x$
$\Rightarrow$ $- a = 1$
$\Rightarrow$ $a = - 1$

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(3 x - 4) (5 x + 7) = 15 x^{2} - a x - 28

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