1.
Expand and simplify: (8g - 3)(7 - 3g).
Correct answer: C. (8g - 3)(7 - 3g) = 56g - 24g² - 21 + 9g = -24g² + 65g - 21.
2.
Expand and simplify: (6p + 3)(5p - 6).
Correct answer: B. (6p + 3)(5p - 6) = 30p² - 36p + 15p - 18 = 30p² - 21p - 18.
3.
Harpreet is 8 years older than Jennifer. The product of their ages is 153. Which equation should be used to solve the problem?
Correct answer: D. Let Jennifer's age be j. Since Harpreet is 8 years older, Harpreet's age is j + 8. The product of their ages is 153, so the equation is j(j + 8) = 153. The solution page lists C, but this appears to be a typo because the equation shown in the solution is j(j + 8) = 153.
4.
Simplify: (2x - y)(3x + 2y).
Correct answer: E. (2x - y)(3x + 2y) = 6x² + 4xy - 3xy - 2y² = 6x² + xy - 2y².
5.
Expand and simplify: (6p + 3)(6p - 7) - (7p - 4)(p - 2).
Correct answer: C. (6p + 3)(6p - 7) = 36p² - 42p + 18p - 21 = 36p² - 24p - 21. (7p - 4)(p - 2) = 7p² - 14p - 4p + 8 = 7p² - 18p + 8. Then (36p² - 24p - 21) - (7p² - 18p + 8) = 36p² - 24p - 21 - 7p² + 18p - 8 = 29p² - 6p - 29.
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