Question

Choose the correct simplification of the expression (−2x + 4y)(3x − 7y). −6x2 − 2xy − 28y2 6x2 + 26xy − 28y2 −6x2 + 26xy + 28y2 −6x2 + 26xy − 28y2

Answer 1

`(-2x+ 4y)(3x - 7y)=-6x^2+26xy-28y^2`

Explanation:

We multiply each term in the parentheses, by those of the other parenthesis:

`(-2x+ 4y)(3x - 7y)=(-2x)(3x)+(-2x)(-7y)+(4y)(3x)+(4y)(-7y)\\=-6x^2+14xy+12xy-28y^2`

Now, we simplify.

We have two terms that contain xy:

`=-6x^2+26xy-28y^2`

Wich will be the correct simplification of the expressionn
`(-2x+ 4y)(3x - 7y)`

Answer 2

`- 6 {x}^(2) + 26xy - 28 {y}^(2)`

Explanation:

The given expresion is:

(−2x + 4y)(3x − 7y)

We expand using the distributive property: (a+b)(c+d)=a(c+d)+b(c+d)

We apply this property to get:

`( - 2x + 4y)(3x - 7y) = - 2x *(3x - 7y) + 4y(3x - 7y)`

We expand further to obtain:

`- 6 {x}^(2) + 14xy + 12xy - 28 {y}^(2)`

`- 6 {x}^(2) + 26xy - 28{y}^(2)`