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

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

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

factor

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

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

Solution steps

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

Factor

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

= x^{2} (x + 2)^{2} - a^{4}

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

a^{4} = (a^{2})^{2}

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

Apply Difference of Two Squares Formula:

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

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

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

Simplify

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

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

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

\frac{x ^{2} + 4 x - 5}{x - 1}

\frac{( x - 1 ) ^{2}}{4 + x ^{2} - 1 + ( x + 1 ) ^{2}}

x^{4} + x^{3} - 3 x^{2} - 5 x - 2

a - 8 a \cdot b^{3}

f (x) - 4 x^{2} + 100 x - 60

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