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expand (x+3)^4

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

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ddx

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

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expand (x+3)⁴

Solution

x⁴+12x³+54x²+108x+81

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Solution steps

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(x+3)⁴

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

a=x, b=3

=∑_i=0⁴(4i)x⁽⁴⁻ⁱ⁾· 3ⁱ

Expand summation

=4!0!(4−0)! x⁴· 3⁰+4!1!(4−1)! x³· 3¹+4!2!(4−2)! x²· 3²+4!3!(4−3)! x¹· 3³+4!4!(4−4)! x⁰· 3⁴

Simplify 4!0!(4−0)! x⁴· 3⁰: x⁴

Simplify 4!1!(4−1)! x³· 3¹: 12x³

Simplify 4!2!(4−2)! x²· 3²: 54x²

Simplify 4!3!(4−3)! x¹· 3³: 108x

Simplify 4!4!(4−4)! x⁰· 3⁴: 81

=x⁴+12x³+54x²+108x+81

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

expand (x+3)^4

Solution

Solution steps

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