SOLUTION: Write an explanation for a student in Mathematics 30-1 about how to expand (a+b)^3. Fully describe two methods of expanding the power of the binomial

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Question 1194665: Write an explanation for a student in Mathematics 30-1 about how to expand (a+b)^3. Fully describe two methods of expanding the power of the binomial
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52778)   (Show Source):
You can put this solution on YOUR website!
.

Look at your textbook, first.

Alternatively, look at the lesson at this site

    - The cube of the sum formula

If your wish to see many sources exceeds two sources, you may extend your search to these sources

https://www.math-only-math.com/expansion-of-a-plus-minus-b-whole-cube.html#:~:text=We%20will%20discuss%20here%20about,(a%20%C2%B1%20b)3.&text=%3D%20a3%20%2B%203a2b,%2B%203ab2%20%2B%20b3.&text=%3D%20a3%20%2D%203a2b,%2B%203ab2%20%2D%20b3.

https://www.mathway.com/popular-problems/Algebra/202987

https://byjus.com/questions/expand-a-b-3/

https://ncalculators.com/algebra/a-b-n-formula-expansion.htm

Happy learning (!)

Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!

You can use the Binomial Theorem to expand out (a+b)^3
More detail about that can be found here
https://www.mathsisfun.com/algebra/binomial-theorem.html
You should find that
(a+b)^3 = a^3+3a^2b+3ab^2+b^3

Here's another approach:
(a+b)^2 = a^2+2ab+b^2 by the FOIL rule
(a+b)^3 = (a+b)(a+b)^2
(a+b)^3 = (a+b)(a^2+2ab+b^2)
(a+b)^3 = c(a^2+2ab+b^2)
(a+b)^3 = c(a^2)+c(2ab)+c(b^2)
(a+b)^3 = a^2(c) + 2ab(c) + b^2(c)
(a+b)^3 = a^2(a+b) + 2ab(a+b) + b^2(a+b)
(a+b)^3 = a^2(a)+a^2(b)+2ab(a)+2ab(b)+b^2(a)+b^2(b)
(a+b)^3 = a^3+a^2b+2a^2b+2ab^2+ab^2+b^3
(a+b)^3 = a^3+3a^2b+3ab^2+b^3

I let c = a+b so we could use the distribution rule.

Take notice that the coefficients are 1, 3, 3, 1 which are found in Pascal's Triangle.

You can use the box method as a way to visually organize the terms
More info found here:
https://www.algebra.com/tutors/box-method.lesson
https://www.onlinemath4all.com/multiplying-polynomials-box-method.html