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Popular >

expand (1+2x)^4

Solution

expand

(1 + 2 x)^{4}

Solution

1 + 8 x + 24 x^{2} + 32 x^{3} + 16 x^{4}

Solution steps

(1 + 2 x)^{4}

Apply binomial theorem:

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

a = 1, b = 2 x

= i = 0 \sum 4 (i 4) \cdot 1^{(4 - i)} (2 x)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 1^{4} (2 x)^{0} : 1

Simplify

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

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 1^{2} (2 x)^{2} : 24 x^{2}

Simplify

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

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 1^{0} (2 x)^{4} : 16 x^{4}

= 1 + 8 x + 24 x^{2} + 32 x^{3} + 16 x^{4}

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Frequently Asked Questions (FAQ)

What is expand (1+2x)^4 ?
The solution to expand (1+2x)^4 is 1+8x+24x^2+32x^3+16x^4