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

Sagot :

Esther

Answer:

[tex]5x(4x^2 - 49y^2)[/tex] or [tex]5x(2x-7y)(2x+7y)[/tex]

Step-by-step explanation:

[tex]20x^3 - 245xy^2[/tex]

[tex]5x(4x^2 - 49y^2)[/tex]

Check your answer:

[tex]5x(4x^2 - 49y^2)[/tex]

[tex]5x(4x^2) + 5x(-49y^2)[/tex]

[tex]20x^3-245xy^2[/tex]

[tex]5x(4x^2 - 49y^2)[/tex] can also be written as:

[tex]5x(4x^2 - 49y^2)[/tex]

[tex]5x(2x-7y)(2x+7y)[/tex]

[tex]5x(4x^2+14xy-14xy+49y^2)[/tex]

[tex]5x(4x^2+49y^2)[/tex]

[tex]5x(4x^2) + 5x(-49y^2)[/tex]

[tex]20x^3-245xy^2[/tex]

Hope this helps!

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

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