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# Algebra Formulas Cheat Sheet page 3

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## Algebra Formula cheat sheet

 Monomials-Raising monomials to a power Multiply the exponent in the parentheses by the power. ( a2 b4 c3 )2 (a2)2=a4 (b4)2=b8 (c3)2=c6 Combine after multiplying by the power a4 b8c6 Multiplying signed numbers   The Rules (+) • (+) = (+) (+) • (-) = (-) (-) • (+) = (-) (-) • (-) = (+) Order of Operations PEMDAS Parentheses Exponents Multiply/Divide(left to right) Add Subtract (left to right) Plotting points on the coordinate plane Step 1 Start at the origin. Find the x-axis, count right for positive and left for negative x value Step 2 Find the y-axis, count up for positive and down for negative y value. Step 3 Write the location of this point Plot (6 -4)   Step 1 Begin at (0,0) move 6 to the right If it was negative you would move to the left Step 2. Move down since it is negative Step 3 Plot the point Polynomial multiplied by -1 When you multiply by -1 you simply change the sign of every term listed. -1(4a + 3b - 3c) = -4a -3b + 3a

 Polynomial multiplied by a monomial Multiply each term by the monomial Combine terms 2x(3x2 + 2x -3) 2x(3x2) = 6x3 2x(2x) = 4x2 2x(-3) = -6x Combine any like and list from largest exponent in order:   6x3 + 4x2 -6 Polynomial multiplied by a variable Step 1 Multiply each term by the variable remember to add the exponents.   Step 2 Combine. x(3x2 + 2x -3) x(32) = 3x3 x(2x) = 2x2 x(-3) = -3x Combine 3x3 + 2x2 -3x Polynomial multiplied by an integer Step 1: Multiply each term by the integer changing only the coefficients.   Step 2: Combine terms 2(3x2 + 2x -3) 2(3x2) = 6x2 2(2x) = 4x 2(-3) = -6 Combine 6x^2 + 4x -6 Polynomials-Adding Polynomials Step 1 Arrange in descending order of exponents Step 2 Combine terms with like variables and exponents Combine -3x8-6x9-4x9+8x+7x8-2x Step1 6x9-4x9 + 3x8 - 7x8 + 8x - 2x Step 2 2x9+ 4x8+ 6x Polynomials-Degree of a polynomial The highest exponent after being simplified 24 – 53 – 10x + 7 is a fourth degree polynomial 27 – 53 – 102 + 7 is a seventh degree polynomial Polynomials-Subtracting Polynomials Set up the problem vertically in descending order Change the bottom signs and add 15x3 - 10x2 + 3- (10x3 + 30x2 + 2) ...................................................... 15x3 - 10x2 + 3 -(10x3+ 30x2 + 2) ............................................................ 15x3 - 10x2 + 3 -10x3 - 30x2 - 2 ­­­­­­­­­­­­­­­­­­­­­­________________ 5x3 - 40x2 + 1 Property-Associative property a + (b + c) = (a + b) + c Changing groupings Ex. 2 + (5 + 3) = (2 + 5) + 3 Property-Commutative property a + b = b + a Ex. 7 + 3 = 3 + 7 Property-Distributive property Multiply the terms inside the parenthesis by the term on the outside of the parenthesis c(a + b) = ca + cb 3(c - b) = 3c -3b Quadratic Equation ax2 + bx + c = 0 a, b, and c are known values x =variable 3x2 + 4x + 3 =0

Free Algebra Cheetsheet with over 40 Algebra Formulas.