Question
Simplify:
$(5 x-3)(x+4)-(2 x+5)(3 x-4)$
$(5 x-3)(x+4)-(2 x+5)(3 x-4)$
✓
Answer
$(5 x-3)(x+4)$
$=5 x(x+4)-3(x+4)$
$=5 x^{(1+1)}+20 x-3 x-12$
$=5 x^2+17 x-12$
$(2 x+5)(3 x-4)$
$=2 x(3 x-4)+5(3 x-4)$
$=6 x^{(1+1)}-8 x+15 x-20$
$=6 x^2+7 x-20$
$\therefore(5 x-3)(x+4)-(2 x+5)(3 x-4)$
$=5 x^2+17 x-12-\left(6 x^2+7 x-20\right)^{\prime}$
$=5 x^2-6 x^2+17 x-7 x-12+20$
$=-x^2+10 x+8$
$=5 x(x+4)-3(x+4)$
$=5 x^{(1+1)}+20 x-3 x-12$
$=5 x^2+17 x-12$
$(2 x+5)(3 x-4)$
$=2 x(3 x-4)+5(3 x-4)$
$=6 x^{(1+1)}-8 x+15 x-20$
$=6 x^2+7 x-20$
$\therefore(5 x-3)(x+4)-(2 x+5)(3 x-4)$
$=5 x^2+17 x-12-\left(6 x^2+7 x-20\right)^{\prime}$
$=5 x^2-6 x^2+17 x-7 x-12+20$
$=-x^2+10 x+8$
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