What is factor t^{12}-r^3s^{15} ?

The solution to factor t^{12}-r^3s^{15} is (t^4-rs^5)(t^8+t^4rs^5+r^2s^{10})

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factor t^{12}-r^3s^{15}

factor

t^{12} - r^{3} s^{15}

(t^{4} - r s^{5}) (t^{8} + t^{4} r s^{5} + r^{2} s^{10})

Solution steps

t^{12} - r^{3} s^{15}

Rewrite

r^{3} s^{15}

(r s^{5})^{3}

= t^{12} - (r s^{5})^{3}

Apply exponent rule:

a^{b c} = (a^{b})^{c}

t^{12} = (t^{4})^{3}

= (t^{4})^{3} - (r s^{5})^{3}

Apply Difference of Cubes Formula:

x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})

(t^{4})^{3} - (r s^{5})^{3} = (t^{4} - r s^{5}) (t^{8} + t^{4} r s^{5} + (r s^{5})^{2})

= (t^{4} - r s^{5}) (t^{8} + t^{4} r s^{5} + (r s^{5})^{2})

Simplify

(t^{4} - r s^{5}) (t^{8} + t^{4} r s^{5} + (r s^{5})^{2}) : (t^{4} - r s^{5}) (t^{8} + t^{4} r s^{5} + r^{2} s^{10})

= (t^{4} - r s^{5}) (t^{8} + t^{4} r s^{5} + r^{2} s^{10})

\frac{2 \cdot 5 - 4}{5 - 5}

4 (x y)

- 6 e + 6 f - 8

x^{6} - 3 x^{4} + 3 x^{2} - 1

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

What is factor t^{12}-r^3s^{15} ?
The solution to factor t^{12}-r^3s^{15} is (t^4-rs^5)(t^8+t^4rs^5+r^2s^{10})