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 Amsco Integrated Algebra I: Multiplying by a Monomial
This is a free lesson from our course in Amsco's Integrated Algebra
 
   
This lesson explains how to multiply a monomial with monomial and a monomial with a polynomial. You have learnt earlier about commutative and associative properties; & the meaning of brackets (or parentheses), when used in algebraic expressions. In any application of brackets, you can use what is known as distributive law. E.g. x (y + z) = xy + xz. It simply means that by placing ‘y + z’ inside the brackets and multiplying the bracketed expression by ‘x’, every term inside the brackets is to be multiplied by ‘x’. That is, we are distributing the factor ‘x’ to all of the terms inside the brackets. Here the process of eliminating a pair of brackets is called expanding the brackets.
 (More text below video...)
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Dividing by a Binomial
(Continued from above) To multiply a monomial with monomial, follow the below given steps:
• use commutative and associative properties to rearrange and group the factors.
• multiply the numerical coefficients.
• multiply powers with the same base by adding exponents.
• multiply the product obtained in just above two steps and any other variable factor by writing them with no sign between them.
For example: (5x)(6y)=(5)(6)(x)(y)=(5*6)(x*y)=30xy.
To multiply a monomial with polynomial, follow the below given steps:
• use distributive property.
• multiply each term of polynomial by the monomial.
• write result as sum of the above products. For example: x(4x+3)=x(4x)+x(3)=4x2+3x.
Have a look at above video for further explanations.
 
   

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