Question

4² + 82x - 2xy - 4yz (Factorize)​

Answer 1

Answer:

We know that one of the identity is (a+b+c)(a

2

+b

2

+c

2

−ab−bc−ca)=a

3

+b

3

+c

3

−3abc

Now, consider the given expression (2x+y+4z)(4x

2

+y

2

+16z

2

−2xy−4yz−8zx) and compare it with the above identity as shown below:

(2x+y+4z)(4x

2

+y

2

+16z

2

−2xy−4yz−8zx)

=(2x+y+4z)[(2x)

2

+y

2

+(4z)

2

−(2x×y)−(y×4z)−(2x×4z)]

=(2x)

3

+y

3

+(4z)

3

−(3×2x×y×4z)

=8x

3

+y

3

+64z

3

−24xyz

Hence, (2x+y+4z)(4x

2

+y

2

+16z

2

−2xy−4yz−8zx)=8x

3

+y

3

+64z

3

−24xyz.