Factor the following polynomial completely. -x 2 y 2 + x 4 + 4y 2 - 4x 2

Mathematics

2 answers:

zlopas [31]4 years ago

5 0

Answer:

$(x + y)(x - y) (x + 2)(x - 2)$

Step-by-step explanation:

$-x^2 y^2 + x^4 + 4y^2 - 4x^2$

Lets rearrange the terms

$x^4 -x^2 y^2 - 4x^2 + 4y^2$

Then we group first two terms and last two terms

$(x^4 -x^2 y^2)+(- 4x^2 + 4y^2)$

Factor out each group

$x^2(x^2 - y^2) - 4 (x^2 - y^2)$

$(x^2 - y^2)(x^2 - 4)$

Apply formula $a^2 - b^2 = (a+b)(a-b)$

$(x + y)(x - y) (x + 2)(x - 2)$

fgiga [73]4 years ago

3 0

<span>-x^2 y^2 + x^4 + 4y^2 - 4x^2
= </span>x^4 -x^2 y^2 - 4x^2 + 4y^2<span>
= x^2 (x^2 - y^2) - 4 (x^2 - y^2)
= (x^2 - y^2)(x^2 - 4)
= (x + y)(x - y) (x + 2)(x - 2) (....using a^2 - b^2 = (a+b)(a-b) )

hope it helps</span>

You might be interested in

If the terms of a polynomial do not have a GCF, does that mean it is not factorable?

JulijaS [17]

Answer:

If the terms of a polynomial do not have a GCF, does that mean it is not factorable? Explain. The terms of a polynomial do not have to have a common factor for the entire polynomial to be factorable.

glad i could help

6 0

3 years ago

Read 2 more answers

Rays QR and QS are tangents to circle P at R and S. If Q measures to 54°, find RS

Ainat [17]

Answer: $126^{\circ}$

Step-by-step explanation:

If we draw RP and PS, then in the quadrilateral formed, we know that $\angle PRQ=\angle PSQ=90^{\circ}$ , and since angles in a quadrilateral add to 360 degrees, this means $\angle SPR=126^{\circ}$ .