Lesson 2 of 3
Distinguish repeated multiplication from distribution across sums.
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Big ideas · 1 of 8
Big ideas
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For a positive whole-number exponent n, means n factors of a multiplied together. Parentheses show whether a sign or coefficient belongs to the base.
A product of sums needs every term from one factor multiplied by every term from the other. Collect like terms only after distributing.
The identity comes from multiplying two complete binomials. A square does not distribute over addition.
Substitution at a convenient input can catch a missed term. A justified expansion uses distribution, not just one numerical check.
Step-through
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Worked example: multiply two binomials
Whole picture, 4 steps
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Do this: Cover the next step and try it yourself.
The middle term comes from two cross-products.
Do this: Explain why the tempting shortcut fails.
Wrong idea: . Squaring means multiplying (x+5)(x+5), so the two cross-products add . The full expansion is .
Worked example
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Worked example
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Watch
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Ready when you are.
Activity 1 of 7 · 0 of 7 activities done
Flashcards
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Card 1 of 8
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The exponent counts factors.
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Write as repeated multiplication.
3 times 3 times 3 times 3.
Evaluate .
−8.
Evaluate .
16.
Expand x(x+7).
.
Expand (x+2)(x+5).
.
Expand .
.
Expand (x+4)(x−4).
.
How can substitution help check an expansion?
It can expose a disagreement at a chosen input, though one match is not a proof.
True or false
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Self-test
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6 questions. One at a time.
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Self-test
Do this: Try each problem without a timer. Read the feedback before moving on.
6 questions. One at a time.
Practice, not a grade. No timer. Your best score stays in this browser.
Write it
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Start here if it helps: I would first identify...
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Write it
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Match
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Connect the ideas
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Homework · 3 points
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Homework
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https://gradebridge-beryl.vercel.app/learn/precalculus/essential-review/exponents-and-products#homework
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