Algebra Periodic Table of the Elements EXPANDING a (b + c) = ab + ac (a – b)2 = a2 – 2ab + b2 (a + b)2 = a2 + 2ab + b2 (a + b) (c + d) = ac + ad + bc + bd (a + b)3 = a3 + 3a2b + 3ab2 + b3 (a – b)3 = a3 – 3a2b + 3ab2 – b3 FACTORING a2 – b2 = (a + b) (a – b) a3b – ab = ab (a + 1) (a – 1) a2 + 2ab + b2 = (a + b)2 a3 + b3 = (a + b) (a2 – ab + b2) a2 – 2ab + b2 = (a – b)2 a3 – b3 = (a – b) (a2 + ab + b2) ROOTS OF A QUADRATIC The solution for a quadratic equation in the form of ax2 + bx + c = 0 can be found by using the quadratic formula: x-axis y-axis quadrant -5 -4 -3 -2 -1 0 1 2 3 4 5 5 4 3 2 1 -1 -2 -3 -4 -5 (4,3) (4,-3) (-4,-3) (-4,3) THE COORDINATE PLANE Commutative property of addition a + b = b + a Commutative property of multiplication ab = ba Associative property of addition a + (b + c) = (a + b) + c Associative property of multiplication a(bc) = (ab)c Distributive property of multiplication over addition a(b + c) = ab + ac Distributive property of multiplication over subtraction a(b – c) = ab – ac PROPERTIES OF ADDITION AND MULTIPLICATION x = –b + b2 – 4ac =+++++++++++ 2a x-axis -5 -4 -3 -2 -1 0 1 2 3 4 5 3 2 1 -1 -2 -3 -4 -5 (4,-3) (-4,-3) a– p = 1 (a 0) ap 1 2 3 4 5 6 7 8 apaq = ap+q ap aq = ap–q a0 = 1 (a 0) (ap)q = apq (ab)p = apbp a p = q ap q =+++ If a, b e R, a, b 0 and p, q e Q, then: LAW OF EXPONENTS a p= ap (b 0) (b) bp (a 0) RESOURCE PAGES R–11
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