Question

factorise 125x^3-64y^3

Answer 1

125x³-64y³
=(5x)³-(4y)³
now,
5x³-4y³ [identity:a³-b³=(a-b)[a²+ab+b²]
(5x-4y)[(5x)²+(4y)²+5x×4y]
(5x-4y)[25x²+16y²+20xy]
hope this answer will help you.

Answer 2

Given:

An algebraic expression 125x³ - 64y³.

To Find:

The factorized form of the given expression is?

Solution:

The given problem can be solved using standard algebra expansions.

1. The given expression 125x³ - 64y³.

2. The expression x³ -y³ can be written as

• (x³ -y³) = ( x - y )( x² + x y + y² ).

3. Use the above formula to expand the given expression.

=> 125x³ - 64y³ = 5³x³ - 4³y³,

=> 5³x³ - 4³y³ = (5x-4y)(25x² + 5x * 4y + 16y²),

=> 5³x³ - 4³y³ = (5x-4y)(25x² + 20x y + 16y²),

4. The expansion of 125x³ - 64y³ is (5x-4y)(25x² + 20x y + 16y²).

Therefore, the factorization of 125x³ - 64y³ is (5x-4y)(25x² + 20x y + 16y²).