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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)} (- 2)^{i}

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

Popular Examples

factor 15h^2-17h-4 factor

15 h^{2} - 17 h - 4

factor 4x^2+36x+32 factor

4 x^{2} + 36 x + 32

simplify (20!)/(14!6!)simplify

\frac{20 !}{14 ! 6 !}

factor 4x^2+18x+20 factor

4 x^{2} + 18 x + 20

3 x = 4.5

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