Simplify: (2x + 5y)(3x + 4y) - (7x + 3y)(2x + y) - Vidyadip

Question

Simplify: $(2x + 5y)(3x + 4y) - (7x + 3y)(2x + y)$

✓

Answer

$(2 x+5 y)(3 x+4 y)$
$=2 x(3 x+4 y)+5 y(3 x+4 y)$
$=6 x^{(1+1)}+8 x y+15 y x+20 y^{(1+1)}$
$=6 x^2+23 x y+20 y^2$
$(7 x+3 y)(2 x+y)$
$=7 x(2 x+y)+3 y(2 x+y)$
$=14 x^{(1+1)}+7 x y+6 y x+3 y$
$=14 x^2+13 x y+3 y^2$
$\therefore(2 x+5 y)(3 x+4 y)-(7 x+3 y)(2 x-y)$
$=6 x^2+23 x y+20 y^2-\left(14 x^2+13 x y+3 y^2\right)$
$=6 x^2-14 x^2+23 x y-13 x y+20 y^2-3 y^2$
$=-8 x^2+10 x y+17 y^2$

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