قم بتحليل التعابير الجبرية التالية إلى عواملها باستخدام طريقة التجميع والعامل المشترك
A
A = (3x + 1)(5x + 3) + (3x + 1)(2x + 2)
\[A = (3x + 1)(5x + 3) + (3x + 1)(2x + 2)\]
\[= (3x + 1)[(5x + 3) + (2x + 2)]\]
\[= (3x + 1)(7x + 5)\]
B
B = (5x + 11)(4y - 1) + (5x + 11)(3y + 2)
\[B = (5x + 11)(4y - 1) + (5x + 11)(3y + 2)\]
\[= (5x + 11)[(4y - 1) + (3y + 2)]\]
\[= (5x + 11)(7y + 1)\]
C
C = (7x - 3)(x + 1) + (7x - 3)(2x + 2)
\[C = (7x - 3)(x + 1) + (7x - 3)(2x + 2)\]
\[= (7x - 3)[(x + 1) + (2x + 2)]\]
\[= (7x - 3)(3x + 3)\]
D
D = (8x - 2)(2 - x) + (2x + 5)(4x - 1)
\[D = (8x - 2)(2 - x) + (2x + 5)(4x - 1)\]
\[= -(8x - 2)(x - 2) + (2x + 5)(4x - 1)\]
\[(8x - 2)(x - 2) = 8x^2 - 16x - 2x + 4 = 8x^2 - 18x + 4\]
E
E = (x - 2)(2x + 3) - (x - 2)(2x + 2)
\[E = (x - 2)(2x + 3) - (x - 2)(2x + 2)\]
\[= (x - 2)[(2x + 3) - (2x + 2)]\]
\[= (x - 2)(1)\]
F
F = (2x - 1)(2 + x) + 3(2 + x)
\[F = (2x - 1)(2 + x) + 3(2 + x)\]
\[= (2 + x)[(2x - 1) + 3]\]
\[= (2 + x)(2x + 2)\]
G
G = (x - 3)(x + 1) + (x + 1)²
\[G = (x - 3)(x + 1) + (x + 1)^2\]
\[= (x + 1)[(x - 3) + (x + 1)]\]
\[= (x + 1)(2x - 2)\]
H
H = (5x + 2)(2x + 1) - (5x + 2)(x + 3)
\[H = (5x + 2)(2x + 1) - (5x + 2)(x + 3)\]
\[= (5x + 2)[(2x + 1) - (x + 3)]\]
\[= (5x + 2)(x - 2)\]