Activity
1. Here is a diagram of a rectangle with side lengths and . Use this diagram to show that and are equivalent expressions.
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Adding these together gives .
2. Draw diagrams to help you write an equivalent expression for each of the following:
a.
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The diagram should show partial products that add up to .
b.
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The diagram should show partial products that add up to .
c.
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The diagram should show partial products that add up to .
d.
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The diagram should show partial products that add up to or .
3. Write an equivalent expression for each expression without drawing a diagram. Use the distributive property to help. Remember FOIL for multiplying binomials: Multiply the First terms, the Outer terms, the Inner terms, and the Last terms.
a.
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b.
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Video: Using Diagrams to Find Equivalent Quadratic Expressions
Watch the following video to learn more about using diagrams to find equivalent quadratic expressions.
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Extending Your Thinking
Image 1
Image 2
Are Image 1 and Image 2 equivalent? Explain or show your reasoning.
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Yes, because .
What does this tell you about an equivalent expression for ?
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This shows that an equivalent expression is .
Is there a different non-zero number of 1-by-1 squares that we could use instead that would allow us to arrange the combined figures into a single large rectangle?
Compare your answer:
We could use four 1-by-1 squares. This would give the expression . The rectangle would be .
Self Check
Additional Resources
Multiplying Binomials
Write an expression equivalent to .
Step 1 - Distribute. Use FOIL. Multiply the First terms, Outer terms, Inner terms, and Last terms.
Step 2 - Write out the four terms.
Step 3 - Combine like terms.
Try it
Try It: Multiplying Binomials
Write an expression equivalent to .
Here is how to multiply binomial expressions:
Step 1 - Distribute.
Step 2 - Write out the four terms.
Step 3 - Combine like terms.