Factor: 100 - h^2.
A(h-10)(h+10)
B(10-h)(10-h)
C(h-100)(h+1)
D(10-h)(10+h)
Answer & Solution
Correct answer: D. (10-h)(10+h)
1. Check that the binomial fits the pattern: 100 is 10 squared, and h squared is h squared, so this is a difference of squares.
2. Write the product of conjugates using a equals 10 and b equals h: (10 - h)(10 + h).
3. Check by multiplying: 100 + 10h - 10h - h squared gives back 100 - h squared.
4. Rewriting the original as h squared - 100 first and factoring that instead gives (h - 10)(h + 10), which is a different expression with the opposite sign.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 7 "Factoring", section 7.4 Factor Special Products_
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