Maths

a)
cd³ - d²e - c²de + ce²
= (cd³ - c²de) + (ce² - d²e)
= cd(d² - ce) - e(d² - ce)
= (cd - e) (d² - ce) b)
2p³ - 6q²t + 4pq² - 3p²t
= (2p³ + 4pq²) - (3p²t + 6q²t)
= 2p(p² + 2q²) - 3t(p² + 2q²)
= (2p - 3t) (p² + 2q²) c)
7m³ + mn² - 7m²n - n³
= (7m³ + mn²) - (7m²n + n³)
= m(7m² + n²) - n(7m² + n²)
= (m - n)(7m² + n²) d)
x⁴-x³y + xy⁴-y³x²
= x³(x - y) + xy³(y - x)
= (x - y) (x³ - xy³)
= x (x - y) (x² - y³) e)
2x + 6 + x³ + 3x²
= (x³ + 2x) + (3x² + 6)
= x(x² + 2) + 3(x² + 2)
= (x + 3) (x² + 2) f)
2x³ + x² + 10x + 5
= x²(2x + 1) + 5(2x +1)
= (x² + 5)(2x + 1) g)
12y + 20 - 9y³ - 15y²
= (12y - 9y³) - (15y² - 20)
= 3y(4 - 3y²) - 5(3y² - 4)
= (3y + 5) (4 - 3y²)