Question

Factorize 2y^3+y^2-2y-1

Answer 1

ANSWER:

• Factorisation of the above expression is (2y+1)(y+1)(y-1)

GIVEN:

• P(x) = 2y³+y²-2y-1

TO FIND:

• Factorise the above expression.

SOLUTION:

= 2y³+y²-2y-1

= (2y³+y²)+(-2y-1)

= y²(2y+1)-1(2y+1)

= (2y+1)(y²-1)

= (2y+1)[(y)² -(1)²]

= (2y+1)(y+1)(y-1)

Factorisation of the above expression is (2y+1)(y+1)(y-1)

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