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Additional resources for Algebra in 15 Minutes a Day (Junior Skill Builders)
Each term has a base of a and an exponent of 5, so the base and exponent of your answer is a5. Add the coefﬁcients: 6 + 2 = 8, so 6a5 + 2a5 = 8a5. 2. Each term has a base of p and an exponent of 1. Remember, if a base does not appear to have an exponent, then it has an exponent of 1. The base of your answer is p. Add the coefﬁcients: –2 + 2 = 0, so –2p + 2p = 0p, or simply 0. 3. Each term has a base of q and an exponent of 12, so the base and exponent of your answer is q12. Combine the two plus signs into one plus sign: 23q12 + (+11q12) = 23q12 + 11q12.
What is 4d ÷ 3 – 20 when d = 12? 9. What is (2b + 1)2 when b = –2? 10. What is –5(3a2 – 24) when a = 3? SIMPLIFYING EXPRESSIONS Some expressions may have only one variable, but that variable appears more than once in the expression. For instance, 8x + 2x, or 2(j – 6) – 7j. We have two choices for evaluating these expressions. We can replace every occurrence, or instance, of the variable with its value, or we can simplify the expression ﬁrst and then replace the variable with its value. Example What is 5v – 8v when v = 10?
The coefﬁcient of 4x3 is 4 and the coefﬁcient of 3x3 is 3. 4 + 3 = 7. Our answer has the same base and the same exponent as the bases and exponents of the terms that we have added, so 4x3 + 3x3 = 7x3. TIP: Do not forget to write the base and exponent of your answer. Once you are sure that you are adding like terms, write the base and the exponent of your answer right away. Before finding the sum of 13v7 and 28v7, write v7 as part of your answer, and then find the sum of the coefficients. qxd:JSB 12/18/08 11:45 AM Page 31 adding and subtracting 31 To ﬁnd –8u8 + (+6u8), we must combine a pair of signs.