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Popular >

expand (2x-1)^4

Solution

expand

(2 x - 1)^{4}

Solution

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

Solution steps

(2 x - 1)^{4}

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 4 (i 4) (2 x)^{(4 - i)} (- 1)^{i}

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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