Question

1) (8+x) (8-x)+(x+2)² 2) (9-b)(9+b)-(3-b)(9+3b+b²) 3) (5x-2)(x+1)-(5-2x)²

Answer 1

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Answer 2

Expanding the first term:

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

Expanding the second term:

(x+2)² = x² + 4x + 4

Putting the two together:

(8+x) (8-x) + (x+2)² = (64 - x^2) + (x² + 4x + 4) = 68 + 3x^2 + 4x

Expanding the first term:

(9-b)(9+b) = 81 - b^2

Expanding the second term:

(3-b)(9+3b+b²) = 27 + 9b - 3b^2 - 9b - 3b^2 - b^3 = -b^3 - 6b^2 + 18b + 27

Putting the two together:

(9-b)(9+b)-(3-b)(9+3b+b²) = (81 - b^2) - (-b^3 - 6b^2 + 18b + 27) = b^3 - 5b^2 + 18b + 54

Expanding the first term:

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

Expanding the second term:

(5-2x)² = 25 - 20x + 4x^2

Putting the two together:

(5x-2)(x+1)-(5-2x)² = (5x^2 + 3x - 2) - (25 - 20x + 4x^2) = 9x^2 + 23x - 27