Question

A = 3x (5x + 1) + (5a + 1) (-7x-4) B = (x - 4) (7 - x) + (x + 3) (7 - x) C = (2x + 3) (5x - 1) - x (2x + 3) D = (4x - 5) (x - 3) - (3x - 1) (4x - 5)

Answer 1

A = (5 x + 1) (3 x - 7 x - 4) = (5 x + 1) (- 4 x - 4)

B = (7 - x) (x - 4 + x + 3) = (7 - x) (2 x - 1)

C = (2 x + 3) (5 x - 1 - x) = (2 x + 3) (4 x - 1)

D = (4 x - 5) (x -3 - 3 x + 1) = (4 x - 5) (- 2 x - 2)

Answer 2

To simplify the given expressions, let's perform the indicated operations step by step:

A = 3x(5x + 1) + (5a + 1)(-7x - 4)

Step 1: Distribute the terms inside the parentheses. A = 15x^2 + 3x + (-35ax - 7x - 20a - 4)

Step 2: Combine like terms. A = 15x^2 - (35a + 4)x + (3 - 20a)

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

Step 1: Distribute the terms inside the parentheses. B = 7x - x^2 - 28 + 4x + 21 - 3x - x^2

Step 2: Combine like terms. B = 4x - 2x^2 - 7

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

Step 1: Distribute the terms inside the parentheses. C = 10x^2 + 2x - 3x - 3 - 2x^2 - 3x

Step 2: Combine like terms. C = 10x^2 - 3x^2 - x - 3

C = 7x^2 - x - 3

D = (4x - 5)(x - 3) - (3x - 1)(4x - 5)

Step 1: Distribute the terms inside the parentheses. D = 4x^2 - 12x - 5x + 15 - (12x - 4x - 15x + 5)

Step 2: Combine like terms. D = 4x^2 - 17x + 15 - (3x)

D = 4x^2 - 17x + 15 - 3x

D = 4x^2 - 20x + 15

So, the simplified expressions are:

A = 15x^2 - (35a + 4)x + (3 - 20a) B = 4x - 2x^2 - 7 C = 7x^2 - x - 3 D = 4x^2 - 20x + 15