Question

. Halla la expresión algebraica factorizada en cada caso.

Answer 1

a) x³ - 8*y³ = x³ - (2y)³ = (x - 2y)(x² + x*2y + (2y)²) = (x - 2y)(x² + 2xy + 4y²)

b) (2x)³ + 9*(3y)³ = (2x)³ + (3∛9y)³ = (2x + 3∛9y)((2x)² + (2x)*3∛9y + (3∛9y)²) = (2x + 3∛9y)(4x² + 6∛9xy + 9∛81y²)

c) (p + q)³ - 8*(a+b)³ = (p + q)³ - (2(a+b))³ = ((p + q) - 2(a + b))((p + q)² + (p + q)*2(a+b) + (2(a+b))²) = (p + q - 2a - 2b)(p² + 2pq + q² + 2(pa + pb + qa + qa) + 4(a² + 2ab + b²)) = (p + q - 2a - 2b)(p² + 2pq + q² + 2pa + 2pb + 2qa + 2qa + 4a² + 8ab + 4b²)

d) 27x³ + 125y³ = (3x)³ + (5y)³ = (3x + 5y)((3x)² - (3x)*(5y) + (5y)²) = (3x + 5y)(9x² - 15xy + 25y²)

Saludos.