What is expand (x^2+y^2)^5 ?

The solution to expand (x^2+y^2)^5 is x^{10}+5x^8y^2+10x^6y^4+10x^4y^6+5x^2y^8+y^{10}

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expand (x^2+y^2)^5

expand

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

x^{10} + 5 x^{8} y^{2} + 10 x^{6} y^{4} + 10 x^{4} y^{6} + 5 x^{2} y^{8} + y^{10}

Solution steps

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

Apply binomial theorem:

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

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

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (x^{2})^{3} (y^{2})^{2} : 10 x^{6} y^{4}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (x^{2})^{2} (y^{2})^{3} : 10 x^{4} y^{6}

Simplify

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

Simplify

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

= x^{10} + 5 x^{8} y^{2} + 10 x^{6} y^{4} + 10 x^{4} y^{6} + 5 x^{2} y^{8} + y^{10}

3 \cdot 1028

3 y - 3 y

x^{2} \cdot x^{- 4}

- \frac{11}{10} + (- \frac{7}{4})

lo g_{10} (3.6)

What is expand (x^2+y^2)^5 ?
The solution to expand (x^2+y^2)^5 is x^{10}+5x^8y^2+10x^6y^4+10x^4y^6+5x^2y^8+y^{10}