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**Extra resources for 501 Algebra Questions, 2nd edition**

**Sample text**

2n(3 + −m) = −2n · 3 + −2n · −m] Use the rules for multiplying signed terms. [−2n · 3 + −2n · −m = −6n + +2mn] Substitute the results into the original expression. (6m + −18n) + (3mn + 15m) + (−6n + +2mn) Remove the parentheses. 6m + −18n + 3mn + 15m + −6n + +2mn Use the commutative property of addition to move like terms together. Use the associative property for addition. (6m + 15m) + (3mn + +2mn) + (−6n + −18n) Combine like terms using addition rules for signed numbers. (21m) + (5mn) + (−24n) Adding a negative term is the same as subtracting a positive term.

Substitute the results into the expression. Parentheses are no longer needed. Use the commutative property of addition to put like terms together. Use the associative property for addition. Add the ﬁrst term using the rules for terms with the same signs. Add the second term using the rules for terms with different signs. Substitute the results into the expression. Parentheses are no longer needed. 34 Team-LRN a(a + 4) + 3a2 + −2a + 10 [a(a + 4) = a · a + a · 4] [a · a + a · 4 = a2 + 4a] (a2 + 4a) + 3a2 + −2a + 10 a2 + 4a + 3a2 + −2a + 10 a2 + 3a2 + 4a + −2a + 10 (a2 + 3a2) + (4a + −2a) + 10 [a2 + 3a2 = 4a2] [4a + −2a = 2a] (4a2) + (2a) + 10 4a2 + 2a + 10 501 Algebra Questions 67.

Signs different? Multiply and give the result a negative sign. Consider the second term. Signs different? Divide and give the result a negative sign. To divide by a fraction, you multiply by the reciprocal. 1 (−5)(6) + (−8) ÷ (ᎏ2ᎏ) 1 (−5)(6) + {(−8) ÷ (ᎏ2ᎏ)} [(−5)(6)] [5 · 6 = 30] [(−5)(6) = −30] 1 [(−8) ÷ (ᎏ2ᎏ)] 1 [8 ÷ ᎏ2ᎏ] 1 2 [8 ÷ ᎏ2ᎏ = 8 · ᎏ1ᎏ = 8 · 2 = 16] 1 Substitute the equivalent values into the original expression. Signs the same? Add the value of the terms and give the result the same sign.