Please Factor Completely and show steps.

Question

16x^4 - 64 =

72x^9 + 1125y^12=

9xy^7 z^5 + 27x^8 y^3 z^10 – 36w^4 x^7 z^6 + 81x^3 y^2 z^9 =

250x^3 - 16y^6 =

Answer 1

The expression 16x⁴ - 64

= 16(x⁴ - 4)

= 16[(x²)² - 2²]

= 16(x² - 2)(x² + 2).

Answer 2

The expression 72x⁹ + 1125y¹²

= 9(8x⁹ + 125y¹²)

= 9 [ (2x³)³ + (5y⁴)³ ]

Apply the formula a³ + b³ = ( a + b)(a² - ab + b²)

a = 2x³ and b = 5y⁴

= 9 (2x³ + 5y⁴)[(4x⁶ - 2x³(5y⁴) + 25y⁸]

72x⁹ + 1125y¹² = 9 (2x³ + 5y⁴)(4x⁶ - 10x³y⁴ + 25y⁸).

Answer 3

The expression 250x³ - 16y⁶

= 2 [ 125 x³ - 8y⁶ ]

= 2 [(5x)³ - (2y²)³]

Apply the formula a³ - b³ = ( a - b)(a² + ab + b²)

a = 5x  and b = 2y²

= 2 (5x - 2y²)[(5x)² + 5x(2y²) + (2y²)²]

= 2 (5x - 2y²)(25x² + 10xy² + 4y⁴)

250x³ - 16y⁶ = 2 (5x - 2y²)(25x² + 10xy² + 4y⁴).