Question

Factor the polynomial completely. Check your answer.
20x^3 - 245xy^2

Answer 1

5x(2x - 7y)(2x + 7y)

Explanation:

20x³ - 245xy² ← factor out 5x from both terms

= 5x(4x² - 49y²) ← this is a difference of squares and factors in general as

a² - b² = (a - b)(a + b) , then

4x² - 49y²

= (2x)² - (7y)²

= (2x - 7y)(2x + 7y)

Then

20x³ = 5x(2x - 7y)(2x + 7y) ← in factored form

Answer 2

`5x(4x^2 - 49y^2)` or
`5x(2x-7y)(2x+7y)`

Explanation:

`20x^3 - 245xy^2`

`5x(4x^2 - 49y^2)`

Check your answer:

`5x(4x^2 - 49y^2)`

`5x(4x^2) + 5x(-49y^2)`

`20x^3-245xy^2`

`5x(4x^2 - 49y^2)` can also be written as:

`5x(4x^2 - 49y^2)`

`5x(2x-7y)(2x+7y)`

`5x(4x^2+14xy-14xy+49y^2)`

`5x(4x^2+49y^2)`

`5x(4x^2) + 5x(-49y^2)`

`20x^3-245xy^2`

Hope this helps!