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Day 2: Multiplying Polynomials
To be able to determine the product of polynomials using the distributive property and the box method.
Remember this skill? It is the key to multiplying polynomials!
\(5(x + 3) = 5x + 15\)
You multiply the number outside by every term inside.
To multiply two binomials, you distribute each term from the first binomial to the second one.
\((\textcolor{blue}{x} + \textcolor{red}{2})(x + 5)\)
\(x(x+5)\) + \(2(x+5)\)
Let's solve \((x + 2)(x + 5)\).
// Step 1: Distribute each term
\(=\textcolor{blue}{x(x+5)} + \textcolor{red}{2(x+5)}\)
// Step 2: Multiply
\(= (\textcolor{blue}{x^2 + 5x}) + (\textcolor{red}{2x + 10})\)
// Step 3: Combine like terms
\(x^2 + 7x + 10\)
The Box Method (or Area Model) helps you organize your work visually. It's great for preventing mistakes!
Problem: \((x+2)(x+5)\)
| \(x\) | \(+5\) | |
| \(x\) | ||
| \(+2\) |
Step 1 & 2: Set up the box and multiply.
| \(x\) | \(+5\) | |
| \(x\) | \(x^2\) | \(+5x\) |
| \(+2\) | \(+2x\) | \(+10\) |
Step 3: Combine like terms and write the answer.
\(x^2 + 7x + 10\)
Let's simplify this expression as a class. Pick your favorite method!
\((x - 3)(2x + 4)\)
Multiply a binomial by a trinomial. The Box Method is very helpful here!
\((n + 2)(n^2 - 3n + 1)\)
\(n^3 - n^2 - 5n + 2\)
Try these problems on your handout, starting with green.
Green Level
MULTIPLY: \((x + 6)(x + 3)\)
Yellow Level
MULTIPLY: \((2y - 4)(y - 5)\)
Red Level
MULTIPLY: \((x - 3)(x^2 + 4x - 2)\)
On your handout or a piece of paper, simplify the following expression: