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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

3. Multiplying Polynomials

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Exercise 46 Page 26

Use the Distributive Property.

x^(2m-1)-x^(m-p+1)+x^(m+p)+x^(m+p-1)-x+ x^(2p)

Practice makes perfect

To find the product, we will first use the Distributive Property.

( x^m+x^p)( x^(m-1)-x^(1-p)+x^p)

Distribute ( x^(m-1)-x^(1-p)+x^p)

x^m( x^(m-1)-x^(1-p)+x^p) + x^p( x^(m-1)-x^(1-p)+x^p)

▼

Distribute (x^m) & (x^p)

Distribute x^m

x^m* x^(m-1)-x^m* x^(1-p)+x^m* x^p+x^p(x^(m-1)-x^(1-p)+x^p)

Distribute x^p

x^m* x^(m-1)-x^m* x^(1-p)+x^m* x^p+x^p* x^(m-1)-x^p * x^(1-p)+x^p * x^p

Now we need to use the Product of Powers Property.

x^m* x^(m-1)-x^m* x^(1-p)+x^m* x^p+x^p* x^(m-1)-x^p * x^(1-p)+x^p * x^p

a^m*a^n=a^(m+n)

x^(m+m-1)-x^(m+1-p)+x^(m+p)+x^(p+m-1)-x^(p+1-p)+ x^(p+p)

Add and subtract terms

x^(2m-1)-x^(m-p+1)+x^(m+p)+x^(m+p-1)-x^1+ x^(2p)

a^1=a

x^(2m-1)-x^(m-p+1)+x^(m+p)+x^(m+p-1)-x+ x^(2p)

This expression is the result of the product.

Subchapter links

Exercises p.25-27