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### Course: Algebra (all content)>Unit 10

Lesson 8: Multiplying binomials by polynomials

# Multiplying binomials by polynomials (old)

An old video where Sal gives several examples of polynomial multiplication. Created by Sal Khan.

## Want to join the conversation?

• Would (x+2)(x-7) be x^2 - 5x + 14?
• You are only slightly wrong.
First term is right: x(x) = x^2
Middle term is correct, too: (-7x + 2x) = -5x
But the last term is wrong. You have to multiply 2 and (-7), so it would be -14, not +14
• When he gets the last part of the second problem after he finishes multiplying at , is that the end of the problem? Or do you have to combine like terms and find a real answer?
• I expanded (x+3x^2)^5 and got x^5 +15X^6 +90x^7 +270x^8 +405x^9 +243x^10 but now I can't figure out the answer to this question: Find the coefficient of x^8 in the expansion of (1+ (x+3x^2))^5. Can someone please help me?
• ``a*x^n; a is the coefficient, n is the exponant, x is the base.``

Given:
``(1 + (x + 3•x^2))^5``

Expand:

``(1 + x + 3•x^2)^5(1 + x + 3•x^2)(1 + x + 3•x^2)(1 + x + 3•x^2)(1 + x + 3•x^2)(1 + x + 3•x^2)(9•x^4 + 6•x^3 + 7•x^2 + 2•x + 1)(9•x^4 + 6•x^3 + 7•x^2 + 2•x + 1)(1 + x + 3•x^2)(81•x^8 + 108•x^7 + 162•x^6 + 120•x^5 + 91•x^4 + 40•x^3 + 18•x^2 + 4•x + 1)(1 + x + 3•x^2)(81•x^8 + 108•x^7 + 162•x^6 + 120•x^5 + 91•x^4 + 40•x^3 + 18•x^2 + 4•x + 1)(1 + x + 3•x^2)243•x^10 + 405•x^9 + 675•x^8 + 630•x^7 + 555•x^6 + 331•x^5 + 185•x^4 + 70•x^3 + 25•x^2 + 5•x + 1``

Coefficient of x^8 term = 675
• The method at is nice but I can't make it work for something like:
(4x^2 + y^2)^2

I end up with 16x^2 + 8x^2 * 2y^2 + y ^4 but it should be 16x^2 + 8x^2 * y^2 + y ^4
• Thank you very much, this was very precise and helped me tons!
Thank you so much again!
• I also thought that you can not multiply a number with another number that has a variable.