Polynomials 05: Multiplying Monomials
Polynomials 05: Multiplying Monomials
In this lesson we will begin to multiply polynomials and we will start with monomials, the simplest type. Multiplying polynomials can have many uses, one of which is to find the area of shapes which may change size but keep the same proportions.
Remembering that y⋅y⋅y=y3, we can apply the same principle to 3x2⋅5x. If we break the equation apart we get 3⋅x⋅x⋅5⋅x. We can then sort to get 3⋅5⋅x⋅x⋅x which simplifies to 15x3.
A more complex equation might look like xy⋅4xy2z⋅7x4z2⋅y2z.
This would expand to be x⋅y⋅4⋅x⋅y⋅y⋅z⋅7⋅x⋅x⋅x⋅x⋅z⋅z⋅y⋅y⋅z.
This would sort to be 4⋅7⋅x⋅x⋅x⋅x⋅x⋅x⋅y⋅y⋅y⋅y⋅y⋅z⋅z⋅z⋅z and simplify to be 28x6y5z4.
Of course you don't want to do all that work every time, but there is a simple pattern: Multiply the coefficients and add the exponents of like variables.
When multiplying a monomial by a polynomials we must multiply the monomial by each term in the polynomial. This means that 3x2y(2x+6y2) would be 6x3y+18x2y3. This principle applies regardless of the number of terms in the polynomial. 4ab2c(2a2+5bc2-3c+b2c) multiplies to be 8a3b2c+20ab3c3-12ab2c2+4ab4c2.
Directions for this Lesson:
Watch the video below and complete the practice questions.
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