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Popular >

expand (2-x)^4

Solution

expand

(2 - x)^{4}

Solution

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

Solution steps

(2 - x)^{4}

Apply binomial theorem:

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

a = 2, b = - x

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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