Question

Factorie : 27x³+125y³

Answer 1

Given:

• A algebric expression is given .
• The expression is 27x³+125y³.

To Find:

• The factorised form of 27x³+125y³.

Identity Used:

• a³+b³= (a+b)(a²-ab+b²).

Answer:

Taking the given expression,

= 27x³ + 125y³.

= (3x)³ + (5y)³.

= (3x+5y) { (3x)² - 3x × 5y + (5y)²}

=(3x+5y) (9x²-15xy +25y²).

(Factorised form)

Some more 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)
• a³-b³=(a-b)(a²+ab+b²)