expand (4+u)^5

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

simplify solve for inverse tangent line

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expand (4+u)⁵

Solution

1024+1280u+640u²+160u³+20u⁴+u⁵

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Solution steps

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(4+u)⁵

Apply binomial theorem: (a+b)ⁿ=∑_i=0ⁿ(ni)a⁽ⁿ⁻ⁱ⁾bⁱ

a=4, b=u

=∑_i=0⁵(5i)4⁽⁵⁻ⁱ⁾uⁱ

Expand summation

=5!0!(5−0)! · 4⁵u⁰+5!1!(5−1)! · 4⁴u¹+5!2!(5−2)! · 4³u²+5!3!(5−3)! · 4²u³+5!4!(5−4)! · 4¹u⁴+5!5!(5−5)! · 4⁰u⁵

Simplify 5!0!(5−0)! · 4⁵u⁰: 1024

Simplify 5!1!(5−1)! · 4⁴u¹: 1280u

Simplify 5!2!(5−2)! · 4³u²: 640u²

Simplify 5!3!(5−3)! · 4²u³: 160u³

Simplify 5!4!(5−4)! · 4¹u⁴: 20u⁴

Simplify 5!5!(5−5)! · 4⁰u⁵: u⁵

=1024+1280u+640u²+160u³+20u⁴+u⁵

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Notebook

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

expand (4+u)^5

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