Simplify

Question

1) (4a-2b)*(a+b)

2) (2a-5)^2

3) (x-3)*(x^2-4x-7)

4) (g-4)*(g+7) 

5)(x+2)*(2x+1)*(3x-1)?

Answer 1

1) (4a - 2b)(a+ b)

= 4a(a) + 4a(b) - 2b(a) - 2b(b)

= 4a² + 4ab - 2ab - 2b²

= 4a² + 2ab - 2b²

(4a - 2b)(a+ b) = 4a² + 2ab - 2b².

Answer 2

2) (2a - 5)²

{ Apply the formula (a - b)² = a² + b² - 2ab, in this case a = 2a and b = 5 }

(2a - 5)² = (2a)² + 5² - 2(2a)(5)

= 4a² + 25 - 20a

(2a - 5)² = 4a² - 20a + 25.

Answer 3

3) (x - 3)(x² - 4x - 7)

= x(x²) + x(- 4x) + x( - 7) - 3(x²) - 3(- 4x) - 3( - 7)

= x³ - 4x² - 7x - 3x² + 12x + 21

= x³ - 7x²  + 5x + 21

(x - 3)(x² - 4x - 7) = x³ - 7x²  + 5x + 21.

Answer 4

4) (g - 4)(g + 7)

= g(g) + g(7) - 4(g) - 4(7)

= g² + 7g - 4g - 28

= g² + 3g  - 28

(g - 4)(g + 7) = g² + 3g - 28.

Answer 5

5) (x + 2)(2x + 1)(3x - 1)

= [(x + 2)(2x + 1)](3x - 1)

= [x(2x) + x(1) + 2(2x) + 2(1)](3x - 1)

= (2x² + x + 4x + 2)(3x - 1)

= (2x² + 5x + 2)(3x - 1)

= 2x²(3x) + 2x²(- 1) + 5x(3x) + 5x(- 1) + 2(3x) + 2(- 1)

= 6x³ - 2x² + 15x² - 5x + 6x - 2

= 6x³ + 13x² + x - 2

(x - 2)(2x + 1)(3x - 1) = 6x³ + 13x² + x - 2.