Question

The following steps are used to rewrite the polynomial expression (x+4y+z)(x-7y)

Answer 1

(x+4y+z)(x-7y)=
`x^(2) +4xy+xz-7xy-28y-7yz`
=
`x^(2) -3xy+xz-7yz`

Answer 2

The product
`\left(x+4y+z\right)\left(x-7y\right)=x^2-3xy-28y^2+xz-7yz`

Explanation:

Given expression (x+4y+z) and (x-7y)

We have to find the product of given expression that is
`\left(x+4y+z\right)\left(x-7y\right)`

Consider
`\left(x+4y+z\right)\left(x-7y\right)`

First multiply each term of first bracket with each term of second bracket, we have,

`=xx+x\left(-7y\right)+4yx+4y\left(-7y\right)+zx+z\left(-7y\right)`

Apply plus- minus rule,
`-(-a)=a` , we have,

`=xx-7xy+4xy-4\cdot \:7yy+xz-7yz`

Like terms are terms with same variable having same power.

Adding like terms , we have,

`=xx-3xy-4\cdot \:7yy+xz-7yz`

Simplify, we have,

`=x^2-3xy-28y^2+xz-7yz`

Thus, the product
`\left(x+4y+z\right)\left(x-7y\right)=x^2-3xy-28y^2+xz-7yz`