3. A = 5 (2x - 7) = 10x - 35
B = -4 (-3x + 1) = 12x - 4
C = 4 - 3 (x - 5) = 4 - 3x + 15 = -3x + 19
D = 5x - 5 (-2x + 1) = 5x + 10x - 5 = 15x - 5
E = 2 (3x + 5) - 4 (x + 2) = 6x + 10 - 4x - 8 = 2x + 2
4. A = (x + 3) (x + 4)
= (x × x + x × 4) + (3 × x + 3 × 4)
= (x² + 4x) + (3x + 12)
= x² + 4x + 3x + 12
= x² + 7x + 12
B = (2x - 3) (-x + 2)
= [2x × (-x) + 2x × 2] - [3 × (-x) + 3 × 2]
= [-2x² + 4x] - [-3x + 6]
= -2x² + 4x + 3x - 6
= -2x² + 7x - 6
C = (-4x + 3) (2x + 1)
= (-4x × 2x - 4x × 1) + (3 × 2x + 3 × 1)
= (-4x² - 4x) + (6x + 3)
= -4x² - 4x + 6x + 3
= -4x² + 2x + 3
D = (7x - 2) (5x - 4)
= (7x × 5x - 7x × 4) - (2 × 5x - 2 × 4)
= (35x² - 28x) - (10x - 8)
= 35x² - 28x - 10x + 8
= 35x² - 38x + 8
E = (-3x - 4) (8x - 7)
= -(3x × 8x - 3x × 7) - (4 × 8x - 4 × 7)
= -(24x² - 21x) - (32x - 28)
= -24x² + 21x - 32x + 28
= -24x² -11x + 28
5. A = 5 + (2x - 7) (4 - 3x)
= 5 + (2x × 4 - 2x × 3x) - (7 × 4 - 7 × 3x)
= 5 + (8x - 6x²) - (28 - 21x)
= 5 + 8x - 6x² - 28 + 21x
= -6x² + 21x - 23
B = 3 - (4x + 1) (-x + 2)
= 3 - [4x × (-x) + 4x × 2] + [1 × (-x) + 1 × 2]
= 3 - [4x² + 8x] + [-x + 2]
= 3 - 4x² - 8x - x + 2
= -4x² - 9x + 5
C = 5x - 1 + (2x - 3) (3x + 1)
= 5x - 1 + (2x × 3x + 2x × 1) - (3 × 3x + 3 × 1)
= 5x - 1 + (6x² + 2x) - (9x + 3)
= 5x - 1 + 6x² + 2x - 9x - 3
= 6x² - 2x - 4
D = 4x² - (-5x + 2) (x - 3)
= 4x² - [-5x × x - 5x × (-3)] + [2 × x - 2 × 3]
E = (2x - 3) (x + 5) - 4 (2x - 1)
= (2x × x + 2x × 5) - (3 × x + 3 × 5) - 4 × 2x - 4 × 1
= (2x² + 10x) - (3x + 15) - 8x - 4
= 2x² + 10x - 3x - 15 - 8x - 4
= 2x² + -x - 19
