What is factor 25x^4-10x^2y^2+y^4-100 ?

The solution to factor 25x^4-10x^2y^2+y^4-100 is (5x^2-y^2+10)(5x^2-y^2-10)

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factor 25x^4-10x^2y^2+y^4-100

factor

25 x^{4} - 10 x^{2} y^{2} + y^{4} - 100

(5 x^{2} - y^{2} + 10) (5 x^{2} - y^{2} - 10)

Solution steps

25 x^{4} - 10 x^{2} y^{2} + y^{4} - 100

Factor

25 x^{4} - 10 x^{2} y^{2} + y^{4} : (5 x^{2} - y^{2})^{2}

= (5 x^{2} - y^{2})^{2} - 100

Factor the number:

100 = 1 0^{2}

= (5 x^{2} - y^{2})^{2} - 1 0^{2}

Apply Difference of Two Squares Formula:

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

(5 x^{2} - y^{2})^{2} - 1 0^{2} = ((5 x^{2} - y^{2}) + 10) ((5 x^{2} - y^{2}) - 10)

= ((5 x^{2} - y^{2}) + 10) ((5 x^{2} - y^{2}) - 10)

Apply rule:

(a) = a

(5 x^{2} - y^{2}) = 5 x^{2} - y^{2}

= (5 x^{2} - y^{2} + 10) (5 x^{2} - y^{2} - 10)

cos^{2} (a) - sin^{2} (a)

(2 t^{5} - t^{2})^{2}

\frac{63 x ^{15} y ^{9}}{7 x y ^{11}}

12 \div \frac{4}{3}

\frac{30}{5}

What is factor 25x^4-10x^2y^2+y^4-100 ?
The solution to factor 25x^4-10x^2y^2+y^4-100 is (5x^2-y^2+10)(5x^2-y^2-10)