What is expand (x^2+y^2)^4 ?

The solution to expand (x^2+y^2)^4 is x^8+4x^6y^2+6x^4y^4+4x^2y^6+y^8

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expand (x^2+y^2)^4

expand

(x^{2} + y^{2})^{4}

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

Solution steps

(x^{2} + y^{2})^{4}

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 4 (i 4) (x^{2})^{(4 - i)} (y^{2})^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (x^{2})^{4} (y^{2})^{0} : x^{8}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (x^{2})^{3} (y^{2})^{1} : 4 x^{6} y^{2}

Simplify

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

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (x^{2})^{1} (y^{2})^{3} : 4 x^{2} y^{6}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (x^{2})^{0} (y^{2})^{4} : y^{8}

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

(x + 1) (x + 3)

\frac{169}{25}

lo g_{4} (12 \cdot 3)

1 0^{3.5}

(\frac{1}{256})^{\frac{1}{4}}

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