Factorise 2x3 + 54y3 - 4x - 12y
Factorization is a method of breaking or decomposing any expression or number into smaller expressions or numbers.
Answer: 2x3 + 54y3 - 4x - 12y can be factorised as 2(x + 3y) (x2 – 3xy + 9y2 – 2)
We will use algebraic identity to factorise 2x3 + 54y3 - 4x - 12y.
From the given expression, 2x3 + 54y3 - 4x - 12y
To factorize the given expression we will perform the following steps.
Step 1: Taking out 2 as a common factor we get 2 (x3 + 27y3 - 2x - 6y)
Step 2: On arranging the like terms we get 2 (x3 + 27y3) – 4 (x + 3y)
Step 3: Using the algebraic identity a3 + b3 = (a + b) (a2 – ab + b2), we will factorise (x3 + 27y3). Hence, it can be written as 2 (x + 3y) (x2 – 3xy + 9y2) – 4(x + 3y)
Step 4: We can take x + 3y as a common factor as it is present in both the terms.
(x + 3y) [ 2(x2 – 3xy + 9y2) – 4 ]
⇒ 2(x + 3y) [(x2 – 3xy + 9y2) – 2]
⇒ 2(x + 3y) (x2 – 3xy + 9y2 – 2)