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Solve for (x+y)^3

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3 Answers

(x+y)² =(x+y)(x+y)    Then you FOIL (First, outer, inner, last)

(x+y)² =(x+y)(x+y) = xx + xy + xy + yy [and when you combine like terms] = x² + 2xy + y²

(x+y)3 = (x² + 2xy + y²)(x+y) Then you FOIL (First, outer, inner, last)

(x+y)3 = (x² + 2xy + y²)(x+y) = x2x +2xxy + xy2 + x2y + 2xyy + y2y [and when you combine like terms] = x3 + 3x2y+ 3xy2 + y3

Comments

Thank you, Kristin! How did you make exponents on the computer? I couldn't figure that out.

Use Microsoft Word and hold the control, shift, and equals key for superscript. Hold   the control and equal key only for subscript.

Comment

To make the exponents, use the shortcut for superscripts: Press CTRL+SHIFT+=; then release the 3 keys and type whatever exponent you wish to insert.

If you want to do the caclulations alot quicker, use Pascal's triangle. Let's say you have (x+y)^n. If you take n! and divide it by (n-r)!*r! then you will have the coefficient to each part of the equation. ! is factorial. Lets say you have 5! = 5*4*3*2*1. r would equal the position of the coefficient. In the case of (x+y)^3 the numbers on pascals triangle are 1 3 3 1. Which means the answer is 1*x^3 + 3*(x^2)(y) + 3*(x)(y^2) + 1*y^3. Do you see a pattern with x and y. The numbers in pascals triangle represents how many different combinations can be taken from a limited number of something. (Ex. How many ways can you take 3 employees from 5 employees). The answer would be 10 ways if you use the equation. Here is a more detailed explanation of Factorial. Imagine you have five pieces of candy. If you choose one then you can only choose four more. If you choose another piece of candy then you can only choose three more pieces and so on and so on until you arrive at 1. (5*4*3*2*1). This method will save you so much time if you have to deal with large exponents. If you don't understand I will be happy to explain with more clarity.