Simplify the following:$(3x+4)(2x-3)+(5x-4)(x+2)$.

Given :

The given expression is $(3x+4)(2x-3)+(5x-4)(x+2)$.

To do :

We have to simplify the given expression.

Solution :

We know that,

$(a+b)(c+d)=a(c+d)+b(c+d)$

$(3x+4)(2x-3)+(5x-4)(x+2)= 3x(2x-3)+4(2x-3)+5x(x+2)-4(x+2)$

                                        $= 6x^2 -9x + 8x -12 +5x^2+10x -4x-8$

                                       $= 6x^2 + 5x^2 -x+6x-20$

                                        $= 11x^2+5x-20$

Therefore, the simplified form of the given expression is $ 11x^2+5x-20$.

$\begin{array}{l}$
( 3x+4)( 2x-3) +( 5x-4)( x+2) =3x( 2x-3) +4( 2x-3) +5x( x+2) -4( x+2)\
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =6x^{2} -9x+8x-12+5x^{2} +10x-4x-8\
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =( 6+5) x^{2} +( -9+8+10-4) x+( -12-8)\
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =11x^{2} +5x-20
\end{array}

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Updated on: 10-Oct-2022

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