Question

Answer 1

x³z + x²yz - x²z² - xyz²

= xz(x² + xy - xz - yz)

= xz[(x² + xy) - (xz + yz)]

= xz[x(x + y) - z(x + y)]

= xz(x + y)(x - z)

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a²x + a²y + ax + ay + x + y

= (a²x + a²y) + (ax + ay) + (x + y)

= a²(x + y) + a(x + y) + (x + y)

= (x + y)(a² + a + 1)

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a² + 2ab + b² - c² + 2cd - d²

= (a² + 2ab + b²) - (c² - 2cd + d²)

= (a + b)² - (c - d)²

= [(a + b) - (c - d)][(a + b) + (c - d)]

= (a + b - c + d)(a + b + c - d)

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z² - (x - 1)² + 2(x - 1) - 1

= z² - [(x - 1)² - 2(x - 1) + 1]

= z² - (x - 1 - 1)²

= z² - (x - 2)²

= (z - x + 2)(z + x - 2)

Answer 2