Question

1) a3 + 8b3 2) x2y – 36 y3 3) -5 m2 + 10mn+5n2 4) 4ab – 28b + 8a – 56 5) a4 – 81

Answer 1

1) a³ + 8b³ = a³ + (2b)³ = (a + 2b)(a² - 2ab + b²)

2) x²y - 36y³ = y(x² - 36y²) = y(x - 6y)(x + 6y)

3) - 5m² + 10mn - 5n² = - 5(m² - 2mn + n²) = - 5(m - n)² = - 5(m - n)(m - n)

4) 4ab - 28b + 8a - 56 = (4ab + 8a) - (28b + 56) = 4a(b + 2) - 28(b + 2) =
= (b + 2)(4a - 28) = 4(b + 2)(a - 7)

5) a⁴ - 81 = (a²)² - 9² = (a² - 9)(a² + 9) = (a - 3)(a + 3)(a² + 9)

Answer 2

1) a^3 + 8b^3 = (a + 2b) • (a^2 - 2ab + 4b^2)
2) x^2y - 36y^3 = y • (x - 6y) • (x + 6y)
3) -5m2 + 10mn + 5n2 = -5 • (m^2 - 2mn - n^2)
4) 4ab - 28b + 8a - 56 = 4 (b + 2) • (a - 7)
5) a^4 - 81 = (a - 3) • (a + 3) • (a^2 + 9)

@iGeniusOX⚡