Question

20. Simplify: (3x + 4)(2x - 3) + (5x - 4)(x + 2)​

Answer 1

Answer:

11x²+5x-20

Step-by-step explanation:

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

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

= 6x²-9x+8x-12+5x²+10x-4x-8

= 6x²+5x²-9x+8x+10x-4x-12-8

= 11x²+18x-13x-20

= 11x²+5x-20

Answer 2

Given :

• (3x + 4)(2x - 3) + (5x - 4)(x + 2)
• And asked to simplify.

To find :

• (3x + 4)(2x - 3) + (5x - 4)(x + 2)?

Solution :

$\bf \implies (3x + 4)(2x - 3) + (5x - 4)(x + 2) \\ \\ \bf \implies ({6x}^{2} - 9x + 8x - 12) + (5x - 4)(x + 2) \\ \\\bf \implies ({6x}^{2} - 9x + 8x - 12) +( {5x}^{2} + 10x - 4x - 8) \\ \\ \bf \implies( {6x}^{2} - x- 12 - 8 )+ ({5x}^{2} + 10x - 4x) \\ \\\bf \implies( {6x}^{2} - x - 20) + ({5x}^{2} + 6x ) \\ \\ \bf \implies {11x}^{2} - x - 20 + 6x \\ \\ \bf \implies {11x}^{2} ( - x + 6x) - 20 \\ \\ \bf \implies {11x}^{2} + 5x - 20$

Therefore, (3x + 4)(2x - 3) + (5x - 4)(x + 2) = 11x² + 5x - 20.

[Note - Scroll right to view full answer]

$\boxed{\begin{array}{cc}\boxed{\bigstar\:\:\textbf{\textsf{Algebric\:Identity}}\:\bigstar}\\\\1)\bf\:(A+B)^{2} = A^{2} + 2AB + B^{2}\\\\2)\sf\: (A-B)^{2} = A^{2} - 2AB + B^{2}\\\\3)\bf\: A^{2} - B^{2} = (A+B)(A-B)\\\\4)\sf\: (A+B)^{2} = (A-B)^{2} + 4AB\\\\5)\bf\: (A-B)^{2} = (A+B)^{2} - 4AB\\\\6)\sf\: (A+B)^{3} = A^{3} + 3AB(A+B) + B^{3}\\\\7)\bf\:(A-B)^{3} = A^{3} - 3AB(A-B) + B^{3}\\\\8)\sf\: A^{3} + B^{3} = (A+B)(A^{2} - AB + B^{2})\\\\\end{array}}$