What is expand (2x+1)^5 ?

The solution to expand (2x+1)^5 is 32x^5+80x^4+80x^3+40x^2+10x+1

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expand (2x+1)^5

expand

(2 x + 1)^{5}

32 x^{5} + 80 x^{4} + 80 x^{3} + 40 x^{2} + 10 x + 1

Solution steps

(2 x + 1)^{5}

Apply binomial theorem:

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

a = 2 x, b = 1

= i = 0 \sum 5 (i 5) (2 x)^{(5 - i)} \cdot 1^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (2 x)^{5} \cdot 1^{0} : 32 x^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (2 x)^{4} \cdot 1^{1} : 80 x^{4}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (2 x)^{3} \cdot 1^{2} : 80 x^{3}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (2 x)^{2} \cdot 1^{3} : 40 x^{2}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (2 x)^{1} \cdot 1^{4} : 10 x

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (2 x)^{0} \cdot 1^{5} : 1

= 32 x^{5} + 80 x^{4} + 80 x^{3} + 40 x^{2} + 10 x + 1

lo g_{10} (x)

(x^{2} + 1) (x + 1)

\frac{- 15 x ^{8} y ^{6} z ^{10}}{3 x ^{4} z ^{2}}

3 \times \frac{2}{3}

7 \times 9

What is expand (2x+1)^5 ?
The solution to expand (2x+1)^5 is 32x^5+80x^4+80x^3+40x^2+10x+1