Activity
1. Write each expression in standard form:
Compare your answer:
a.
Compare your answer:
b.
Compare your answer:
c.
Compare your answer:
or
d.
Compare your answer:
2. Decide if each expression is a perfect square. If so, write an equivalent expression of the form . If not, suggest one change to turn it into a perfect square.
a.
Compare your answer:
Yes, a perfect square.
b.
Compare your answer:
No, not a perfect square. Suggested changes include:
- Changing the coefficient of the linear term to 20 gives , which is equivalent to .
- Changing the coefficient of the linear term to -20 gives , which is equivalent to .
- Changing the constant term to 4 gives , which is equivalent to .
Video: Rewrite Squared Expressions
Watch the following video to learn more about rewriting squared expressions.
Self Check
Factoring Perfect Square Trinomials
To factor perfect square trinomials, follow the formulas:
Let's look at an example of how to factor perfect square trinomials.
Example
Factor .
Step 1 - Does the trinomial fit the perfect square trinomial pattern, ? If so, write the first term as and last constant as .
- Is the first term a perfect square? Write it as a square, . Is a perfect square? Yes — write it as .
- Is the last term a perfect square? Write it as a square, . Is 4 a perfect square? Yes — write it as .
- Check the middle term. Is it ? Is twice the product of and 2? Does it match? Yes, so we have a perfect trinomial.
Step 2 - Factor the binomial into: .
Step 3 - Check.
Try it
Try It: Factoring Perfect Square Trinomials
Factor .
Here is how to factor a perfect square trinomial:
Step 1 - Write the first term as and the last constant as .
,
Make sure the middle term is .
Step 2 - Factor the binomial into: .
Step 3 - Check.