عمل ما يلي

7x-49 +14 x² = $7x - 49 + 14x^2 = 7(x - 7 + 2x^2) = 7(2x^2 + x - 7)$

9x +12 x +4 = $9x^2 + 12x + 4 = (3x)^2 + 2 \times 3x \times 2 + 2^2 = (3x + 2)^2$

(2x-7)(x+4) – ( 2x – 7)(4x + 1) = $(2x - 7)(x + 4) - (2x - 7)(4x + 1) = (2x - 7)[(x + 4) - (4x + 1)] =$ $(2x - 7)(x + 4 - 4x - 1) = (2x - 7)(-3x + 3) = 3(2x - 7)(-x + 1)$

(4x-1)² +(2x-5)(4x -1) = $(4x - 1)^2 + (2x - 5)(4x - 1) = (4x - 1)[(4x - 1) + (2x - 5)] =$ $(4x - 1)(4x - 1 + 2x - 5) = (4x - 1)(6x - 6) = 6(4x - 1)(x - 1)$
(x+7)(3x-1) + 7x + 49=
$(x + 7)(3x - 1) + 7x + 49 = (x + 7)(3x - 1) + 7(x + 7) =$ $(x + 7)(3x - 1 + 7) = (x + 7)(3x + 6) = 3(x + 7)(x + 2)$

$16x^2 - 81 = (4x)^2 - 9^2 = (4x - 9)(4x + 9)$

$49x^2 - \frac14 = (7x)^2 - \left(\frac12\right)^2 = \left(7x - \frac12\right)\left(7x + \frac12\right)$

$9x^2 + 30x + 25 = (3x)^2 + 2 \times 3x \times 5 + 5^2 = (3x + 5)^2$

(2x +3)² – 49= $(2x + 3)^2 - 49 = (2x + 3)^2 - 7^2 = [(2x + 3) - 7][(2x + 3) + 7] =$ $(2x - 4)(2x + 10) = 2(x - 2) \times 2(x + 5) = 4(x - 2)(x + 5)$
(4x – 1 )² – (2x + 3 )² =
$(4x - 1)^2 - (2x + 3)^2 = [(4x - 1) - (2x + 3)][(4x - 1) + (2x + 3)] =$ $(4x - 1 - 2x - 3)(4x - 1 + 2x + 3) = (2x - 4)(6x + 2) = 2(x - 2) \times 2(3x + 1) = 4(x - 2)(3x + 1)$

x³ - 16x = $x^3 - 16x = x(x^2 - 16) = x(x^2 - 4^2 ) = x(x - 4)(x + 4)$

$25x^2 - 1 - (4x - 3)(5x + 1) = (5x)^2 - 1 - (4x - 3)(5x + 1) =$ $(5x - 1)(5x + 1) - (4x - 3)(5x + 1) = (5x + 1)[(5x - 1) - (4x - 3)] = (5x + 1)(5x - 1 - 4x + 3) =$ $(5x + 1)(x + 2)$

x² +8x+16 = $x^2 + 8x + 16 = x^2 + 2 \times x \times 4 + 4^2 = (x + 4)^2$

4x²-4x+1= $4x^2 - 4x + 1 = (2x)^2 - 2 \times 2x \times 1 + 1^2 = (2x - 1)^2$

x² -64 = $x^2 - 64 = x^2 - 8^2 = (x - 8)(x + 8)$

x² + x +0,25= $x^2 + x + 0,25 = x^2 + 2 \times x \times 0,5 + 0,5^2 = \left(x + 0,5)^2$

100x² -1000x +2500 = $100x^2 - 1\,000x + 2\,500 = (10x)^2 - 2 \times 10x \times 50 + 50^2 =$

$(10x - 50)^2 = [10(x - 5)^2] = 10^2 (x - 5)^2 = 100 (x - 5)$

16 x² – 81/4 = $16x^2 - \frac{81}{4} = (4x)^2 - \left(\frac92\right)^2 =$ $\left(4x - \frac92\right)\left(4x + \frac92\right)$

2x² +2= $2x^2 + 2 = 2(x^2 + 1)$

(3x – 1)² – (x + 2)²= $(3x - 1)^2 - (x + 2)^2 = [(3x - 1) - (x + 2)][(3x - 1) + (x + 2)] =$ $(3x - 1 - x - 2)(3x - 1 + x + 2) = (2x - 3)(4x + 1)$