Question

Factorise 4x2y - 8xy2

Answer 1

4x2y - 8xy2

$4(x2y - 2xy2 )$

Answer 2

Factors of polynomial $\bf 4 {x}^{2} y - 8x {y}^{2}$ are $\bf \red{4xy(x - 2y)}$.

Given:

• $4 {x}^{2} y - 8x {y}^{2}$

To find:

• Factorise the given polynomial.

Solution:

In factorisation of polynomials, polynomial is written in terms of multiplication of factors.

• Few polynomials can be factorise by taking common terms out.
• Few can be factorise with the help of identity there after
• $\bf {a}^{2}-{b}^{2} =(a-b)(a+b)$
• $\bf {a}^{3}-{b}^{3} =(a-b)(a^2+ab+b^2)$
• $\bf {a}^{3}+{b}^{3} =(a+b)(a^2-ab+b^2)$

Here, in the given polynomial

Take common term out.

$4 {x}^{2} y - 8x {y}^{2}$

4xy is common in both terms, so

$\bf 4 {x}^{2} y - 8x {y}^{2}= 4xy(x - 2y)$

Factors of given polynomial $4 {x}^{2} y - 8x {y}^{2}$ are $4xy(x - 2y)$.

Thus,

Factors are $\bf (4xy)(x - 2y)$.

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