a) (x+1)² + (x+2)² = x² + 2x + 1 + x² + 4x + 4 = 2x² + 6x + 5
b) (x+3)² + (x-2)² = x² + 6x + 9 + x² - 4x + 4 = 2x² + 2x + 13
c) (x-4)² - (x+4)² = x² - 8x + 16 - (x² + 8x + 16) = x² - 8x + 16 - x² - 8x - 16 = -16x
d) (x-3)² - (x-1)² = x² - 6x + 9 - (x² - 2x + 1) = x² - 6x + 9 - x² + 2x - 1 = -4x + 8
e) (2x-1)² - (2x-3)² = (2x)² - 2(2x)(1) + 1 - (2x)² + 2(2x)(3) - 3² = 4x² - 4x + 1 - 4x² + 12x - 9 = 8x - 8
f) (2x+1)² - (3x-1)² = (2x)² + 2(2x)(1) + 1 - (3x)² + 2(3x)(1) - 1² = 4x² + 4x + 1 - 9x² + 6x - 1 = -5x² + 10x
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a) (x+1)² + (x+2)² = x² + 2x + 1 + x² + 4x + 4 = 2x² + 6x + 5
b) (x+3)² + (x-2)² = x² + 6x + 9 + x² - 4x + 4 = 2x² + 2x + 13
c) (x-4)² - (x+4)² = x² - 8x + 16 - (x² + 8x + 16) = x² - 8x + 16 - x² - 8x - 16 = -16x
d) (x-3)² - (x-1)² = x² - 6x + 9 - (x² - 2x + 1) = x² - 6x + 9 - x² + 2x - 1 = -4x + 8
e) (2x-1)² - (2x-3)² = (2x)² - 2(2x)(1) + 1 - (2x)² + 2(2x)(3) - 3² = 4x² - 4x + 1 - 4x² + 12x - 9 = 8x - 8
f) (2x+1)² - (3x-1)² = (2x)² + 2(2x)(1) + 1 - (3x)² + 2(3x)(1) - 1² = 4x² + 4x + 1 - 9x² + 6x - 1 = -5x² + 10x