Question

factorize 2y³ + y² - 2y - 1​

Answer 1

Answer:

2y³ + y² - 2y - 1

y²(2y + 1) -1(2y - 1)

(y²-1)(2y-1)

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Answer 2

ANSWER:

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

GIVEN:

• 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)(y²-1²)

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

If the question asked to find the value of 'y' then:

=> (2y+1)(y+1)(y-1) = 0

Either (2y+1) = 0

=> 2y = (-1)

=> y = -1/2

Either (y+1) = 0

=> y = (-1)

Either (y-1) = 0

=> y = 1

NOTE

some important formulas:

1. (a+b)² = a²+b²+2ab
2. (a-b)² = a²+b²-2ab
3. (a+b)³ = a³+b³+3ab(a+b)
4. (a-b)³ = a³-b³-3ab(a-b)
5. (a³-b³) = (a-b)(a²+b²+ab)