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

The solution to expand (x^2+2x)^4 is x^8+8x^7+24x^6+32x^5+16x^4

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expand (x^2+2x)^4

expand

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

x^{8} + 8 x^{7} + 24 x^{6} + 32 x^{5} + 16 x^{4}

Solution steps

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

Apply binomial theorem:

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

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

= i = 0 \sum 4 (i 4) (x^{2})^{(4 - i)} (2 x)^{i}

Expand summation

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

Simplify

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

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (x^{2})^{3} (2 x)^{1} : 8 x^{7}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (x^{2})^{2} (2 x)^{2} : 24 x^{6}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (x^{2})^{1} (2 x)^{3} : 32 x^{5}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (x^{2})^{0} (2 x)^{4} : 16 x^{4}

= x^{8} + 8 x^{7} + 24 x^{6} + 32 x^{5} + 16 x^{4}

∣ - 5 + 3 ∣

- \frac{5}{6}

- 2 \frac{3}{5}

4.5 \cdot 1 0^{5}

- 14 - (- 5)

What is expand (x^2+2x)^4 ?
The solution to expand (x^2+2x)^4 is x^8+8x^7+24x^6+32x^5+16x^4