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What is the expansion of (x+2)^4?

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vc1596 | Student, Grade 10 | eNotes Newbie

Posted December 19, 2008 at 3:08 AM via web

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What is the expansion of (x+2)^4?

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cburr | Middle School Teacher | (Level 2) Associate Educator

Posted December 19, 2008 at 4:38 AM (Answer #1)

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This problem is straightforward if you take it step by step.

First, (x + 2)^4 = (x + 2) (x + 2) (x + 2) (x + 2)

Step 1 is to begin with (x + 2) (x + 2). To do this, you multiply each of the elements from the first parenthesis times each of the items in the second. So, you get:

x * x = x^2

x * 2 = 2x

2 * x = 2x

2 * 2 = 4

Add these together, and you get x^2 + 4x + 4

Step 2 is to multiply all that first by x:

x^3 + 4x^2 + 4x

and then by 2:

2x^2 + 8x + 8.

Add them all together and you get: x^3 + 6 x^2 + 12x + 8.

Step 3 is to multiply all that by the last (x + 2).

First by x: x^4 + 6x^3 + 12x^2 + 8x

then by 2: 2x^3 + 12 x^2 + 24x +16

Add those two together and simplify for the final answer:

x^4 + 8x^3 + 24x^2 + 32x +16

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mayowa | Student, Undergraduate | eNotes Newbie

Posted December 23, 2008 at 8:49 PM (Answer #2)

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x^4 + 8x^3 + 24x^2 + 32x +16

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dracomath | Student, Grade 11 | (Level 1) Honors

Posted December 28, 2008 at 12:43 AM (Answer #3)

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(x+2)(x+2)(x+2)(x+2)

(x²+4x+4)(x²+4x+4)

x^4+4x³+4x²+4x³+16x²+16x+4x²+16x+16

 x^4+8x³+20x²+32x+16

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revolution | College Teacher | (Level 1) Valedictorian

Posted July 17, 2010 at 10:55 PM (Answer #4)

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Use the binomal theorem:

(x+2)^4= x^4 + 4C1(x)^3(2)^1+ 4C2(x)^2(2)^2+4C3(x)^1(2)^3+(2)^4

= x^4+ 8x^3 + 24x^2 + 32x + 16

This is much faster than expanding (xt2) four times.

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Wiggin42 | Student, Grade 11 | (Level 2) Valedictorian

Posted April 4, 2014 at 8:20 PM (Answer #5)

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(x+2)^4

Is the same as multiplying (x + 2) four times, so we get:

(x+2)(x+2)(x+2)(x+2)

Which is the same as multiplying to binomials: ((x+2)(x+2)) ((x+2)(x+2))

We can apply foil to both sides and multiply each term individually. 

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atyourservice | Student, Grade 10 | (Level 3) Valedictorian

Posted April 16, 2014 at 6:20 PM (Answer #6)

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(x + 2)^4 = (x + 2) (x + 2) (x + 2) (x + 2)

The first thing you do is foil the first 2 parentheses 

 (x + 2) (x + 2) l (x + 2) (x + 2)

(x + 2) (x + 2)

`x^2+2x+2x+4 `

combine like terms:P

`x^2+4x+4 `

Multiply is with the third parenthesis

`(x^2+4x+4)(x+2) `

`x^3+2x^2+4x^2+8x+4x+8 `

combine like terms

`x^3+6x^2+12x+8 `

multiply it by the last parenthesis

(x^3+6x^2+12x+8) (x+2)

`x^4+2x^3+6x^3+12x^2+12x^2+24x+8x+16 `

combine like terms

`x^4+8x^3+24x^2+32x+16 `

and that's the answer

x^4+8x^3+24x^2+32x+16

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acompanioninthetardis | Student, Undergraduate | (Level 1) Valedictorian

Posted May 18, 2014 at 4:06 AM (Answer #7)

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Expansion is just stretching it out so an expansion of x+2^4 would be (x+2)(x+2 )(x+2)(x+2). You then multiply. So you get (x^2 +4x+ 4)(x^2+4x+4) which equals to x^4+8x^3+24x^2+32x+16

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parama9000 | Student, Grade 11 | (Level 1) Valedictorian

Posted May 31, 2014 at 3:53 PM (Answer #8)

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Expansion is to basically to write (x+2) four times in a row and multiply them.

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crystaltu001 | Student, Grade 10 | (Level 1) Valedictorian

Posted July 1, 2014 at 6:55 PM (Answer #9)

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(x+2)^4

You write (x+2) 4 times and then multiply all of them together

(x+2)(x+2)(x+2)(x+2)

You multiply the first 2 first and then when you get the answer for that, you multiply that answer with the next and then the next.

(x+2)(x+2)= x^2+4x+4

(x^2+4x+4)(x+2)= x^3+6x^2+12x+8

(x^3+6x^2+12x+8)(x+2)= x^4+8x^3+24x^2+32x+16

The answer is x^4+8x^3+24x^2+32x+16

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