Question

factorise 8 x^3 +y^3+12yx^2+6xy^2

Answer 1

Given : -

factorise 8 x³ +y³+12yx²+6xy²

Solution : -

By applying identity to solve this factorise

use this identity

(a+b)³=a³+b³+3ab(a+b)

= 8x³ + y³ + 12yx² + 6xy²

= (2x)³ + (y)³ + 3 × 2x × y(2x + y)

= (2x + y)³

Note : -

Some important identities

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

Answer 2

Step-by-step explanation:

8x³ + y³ + 12x²y + 6xy²

=(2x)³ + (y)³ + 3×(2x)²× (y) +3×(y)²×(2x)

= (2x + y)³

Formula Used -

• (a + b)³ = a³ + b³ + 3a²b + 3b²a

Others Formula like this -

• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab + b²
• (a + b)(a - b) = a² - b²
• (a - b)³ = a³ - 3a²b + 3b²a - b³