Question

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

Answer 1

Answer:

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

Step-by-step 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

Answer:

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

Step-by-step 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!