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Popular >

expand (x+1)^4

Solution

expand

(x + 1)^{4}

Solution

x^{4} + 4 x^{3} + 6 x^{2} + 4 x + 1

Solution steps

(x + 1)^{4}

Apply binomial theorem:

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

a = x, b = 1

= i = 0 \sum 4 (i 4) x^{(4 - i)} \cdot 1^{i}

Expand summation

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

Simplify

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

Simplify

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

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} x^{2} \cdot 1^{2} : 6 x^{2}

Simplify

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

Simplify

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

= x^{4} + 4 x^{3} + 6 x^{2} + 4 x + 1

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125 x^{9} - 45 x

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a^{2} + 14 ab + 49 b^{2} - 4

3(4-2x)<-5(x-2)+3

3 (4 - 2 x) < - 5 (x - 2) + 3

7 x + 4 \geq 9 x - 1

simplify (-y^4d^6)^8 simplify

(- y^{4} d^{6})^{8}

Frequently Asked Questions (FAQ)

What is expand (x+1)^4 ?
The solution to expand (x+1)^4 is x^4+4x^3+6x^2+4x+1