What is factor x^4+4x^3+4x^2-y^2 ?

The solution to factor x^4+4x^3+4x^2-y^2 is (x^2+2x+y)(x^2+2x-y)

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factor x^4+4x^3+4x^2-y^2

factor

x^{4} + 4 x^{3} + 4 x^{2} - y^{2}

(x^{2} + 2 x + y) (x^{2} + 2 x - y)

Solution steps

x^{4} + 4 x^{3} + 4 x^{2} - y^{2}

Factor

x^{4} + 4 x^{3} + 4 x^{2} : x^{2} (x + 2)^{2}

= x^{2} (x + 2)^{2} - y^{2}

Apply exponent rule:

a^{n} b^{n} = (a \cdot b)^{n}

x^{2} (x + 2)^{2} = (x (x + 2))^{2}

= (x (x + 2))^{2} - y^{2}

Apply Difference of Two Squares Formula:

x^{2} - y^{2} = (x + y) (x - y)

(x (x + 2))^{2} - y^{2} = (x (x + 2) + y) (x (x + 2) - y)

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

Simplify

(x (x + 2) + y) (x (x + 2) - y) : (x^{2} + 2 x + y) (x^{2} + 2 x - y)

= (x^{2} + 2 x + y) (x^{2} + 2 x - y)

\frac{( - 13 x + 15 x ^{2} - 20 )}{( 3 x - 5 )}

(4 i^{w} \cdot k^{- 3 - n}) (- j \cdot k^{n + 3})

512 x^{3} + 27 y^{3}

(n^{3})^{7}

\frac{121}{144} \cdot x^{8} \cdot y^{6} - \frac{4}{25} \cdot z^{14}

What is factor x^4+4x^3+4x^2-y^2 ?
The solution to factor x^4+4x^3+4x^2-y^2 is (x^2+2x+y)(x^2+2x-y)