Question

Factorise 54xcube - 16ycube

Answer 1

ANSWER:

GIVEN:

• 54x³-16y³

TO FIND:

• Factorise the above expression

SOLUTION:

= 54x³-16y³

= 2(27x³-8y³)

= 2[(3x)³-(2y)³]

= 2(3x-2y)[(3x)²+(2y)²+(3x*2y)]

= 2(3x-2y)(9x²+4y²+6xy)

Factorisation of 54x³-16y³ is 2(3x-2y)(9x²+4y²+6xy)

NOTE:

Some important formulas:

(a+b)² = a²+b²+2ab

(a-b)² = a²+b²-2ab

(a+b)(a-b) = a²-b²

(a+b)³ = a³+b³+3ab(a+b)

(a-b)³ = a³-b³-3ab(a-b)

a³+b³ = (a+b)(a²+b²-ab)

a³-b³ = (a-b)(a²+b²+ab)

(a+b)² = (a-b)²+4ab

(a-b)² = (a+b)²-4ab