What is Multiplication of Monomials by Polynomials?

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What is Multiplication of Monomials by Polynomials?

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Answer 1 · 2015-02-01T12:37:50

It works the same as with numbers. For numbers, you know that $a (b + c)$ $a(b+c)$ equals $a b + a c$ $ab+ac$ .
For the same reason, if you have a monomial and you want to multiplicate it by a polynomial (which is a sum of monomials with some coefficients!), you follow the same rule.

For example, if your monomial is $3 x^{2}$ $3x^2$ , and your polynomial is $3 + 2 x - 5 x^{2} + 8 x^{3}$ $3+2x-5x^2+8x^3$ , the product is
$3 x^{2} (3 + 2 x - 5 x^{2} + 8 x^{3})$ $3x^2(3+2x-5x^2+8x^3)$
you will calculate is as
$3 x^{2} \cdot 3 + 3 x^{2} \cdot 2 x - 3 x^{2} \cdot 5 x^{2} + 3 x^{2} \cdot 8 x^{3}$ $3x^2\cdot 3+3x^2\cdot2x-3x^2\cdot5x^2+3x^2\cdot8x^3$ , which is
$9 x^{2} + 6 x^{3} - 15 x^{4} + 24 x^{5}$ $9x^2 + 6x^3 - 15x^4 + 24x^5$

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What is Multiplication of Monomials by Polynomials?

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