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Popular >

expand (x+2)^4

Solution

expand

(x + 2)^{4}

Solution

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

Solution steps

(x + 2)^{4}

Apply binomial theorem:

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

a = x, b = 2

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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