What is expand (x^2-3y^2)^5 ?

The solution to expand (x^2-3y^2)^5 is x^{10}-15x^8y^2+90x^6y^4-270x^4y^6+405x^2y^8-243y^{10}

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expand (x^2-3y^2)^5

expand

(x^{2} - 3 y^{2})^{5}

x^{10} - 15 x^{8} y^{2} + 90 x^{6} y^{4} - 270 x^{4} y^{6} + 405 x^{2} y^{8} - 243 y^{10}

Solution steps

(x^{2} - 3 y^{2})^{5}

Apply binomial theorem:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = x^{2}, b = - 3 y^{2}

= i = 0 \sum 5 (i 5) (x^{2})^{(5 - i)} (- 3 y^{2})^{i}

Expand summation

= \frac{5 !}{0 ! ( 5 - 0 ) !} (x^{2})^{5} (- 3 y^{2})^{0} + \frac{5 !}{1 ! ( 5 - 1 ) !} (x^{2})^{4} (- 3 y^{2})^{1} + \frac{5 !}{2 ! ( 5 - 2 ) !} (x^{2})^{3} (- 3 y^{2})^{2} + \frac{5 !}{3 ! ( 5 - 3 ) !} (x^{2})^{2} (- 3 y^{2})^{3} + \frac{5 !}{4 ! ( 5 - 4 ) !} (x^{2})^{1} (- 3 y^{2})^{4} + \frac{5 !}{5 ! ( 5 - 5 ) !} (x^{2})^{0} (- 3 y^{2})^{5}

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (x^{2})^{5} (- 3 y^{2})^{0} : x^{10}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (x^{2})^{4} (- 3 y^{2})^{1} : - 15 x^{8} y^{2}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (x^{2})^{3} (- 3 y^{2})^{2} : 90 x^{6} y^{4}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (x^{2})^{2} (- 3 y^{2})^{3} : - 270 x^{4} y^{6}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (x^{2})^{1} (- 3 y^{2})^{4} : 405 x^{2} y^{8}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (x^{2})^{0} (- 3 y^{2})^{5} : - 243 y^{10}

= x^{10} - 15 x^{8} y^{2} + 90 x^{6} y^{4} - 270 x^{4} y^{6} + 405 x^{2} y^{8} - 243 y^{10}

81 a 7 - b^{5}

2 (x - m)^{3} + 4 (x - m) - 5

1 0^{l o g_{100} (x)}

4 x^{4} + 16 x^{3} - 20 x

x^{4} - x^{2} + 144

What is expand (x^2-3y^2)^5 ?
The solution to expand (x^2-3y^2)^5 is x^{10}-15x^8y^2+90x^6y^4-270x^4y^6+405x^2y^8-243y^{10}