MATH 32A Midterm: Math 32A Exam 1

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7 Mar 2019
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Important things i learned before (but may have forgotten) The basic idea behind algebra is rewriting equations and sim- plifying expressions; this includes such things as fac- toring, foiling (i. e. , (a+b)(c+d) = ac+ad+bc+bd), adding fractions (remember to get a common de- a b c d ad + bc. ) and multiplying by nominator, the conjugate (the conjugate of a + b is a b and multiplying gives a2 b2). Below are some basic facts that frequently come up. bd (a + b)(a b) = a2 b2 (a + b)2 = a2 + 2ab + b2 (a b)2 = a2 2ab + b2. Another useful fact is the quadratic formula (also known as the quadratic equation) ax2 + bx + c = 0 x = 2a xaxb = xa+b, xa xb ln(ab) = ln a + ln b, = xa b, ln(cid:0) (xa)b = xab, a b. ) = ln a ln b, and ln(ab) = b ln a.