Expressions and Polynomial Review August 22, 2016
Essential Questions How do I identify the parts of an expression in terms of context? How do I combine like terms? How do I add or subtract polynomials? How do I multiply polynomials? How do I use polynomials to find the area or perimeter of a polygon?
Outline Vocabulary Review Parts of an Expression Evaluating Expressions Adding Polynomials Subtracting Polynomials Multiplying Polynomials Perimeter Area
Vocabulary Review Binomial expression Monomial expression Expression Factor Integer Perimeter Whole Number Polynomial expression
Vocabulary Review Area Degree of Term Terms Coefficients Solution of an equation Inverse operation Variable Constant Standard form of polynomial
Writing Expressions + (add) - (subtract) x (multiply) ✢ (divide) When writing expressions use these words with the following operational signs + (add) - (subtract) x (multiply) ✢ (divide) Add Plus The sum of Subtract Minus The difference of Times Multiplied by The product of Divided by The quotient of
Writing Expressions Examples include: m + 7 The sum of m and 7. or M plus 7. w-6 The difference of w and 6 or W minus 6. h X 9 The product of h and 9. or H times 9. c ✢ 8 The quotient of c and 8. or C divided by 8.
Writing Expressions Example: Tim scored a total of 18 points in the football game, and he scored g points in the second half of the game. Write an expression to determine the number of points he scored in the first half of the game. Then find the number of points he scored in the first half of the game if he scored 12 points in the second half of the game.
Writing Expressions Scored 18 points for entire game Scored g points in the second half 18-g = points in first half g= 12 points in second half 18-(12) = 18-12 = 6 points in first half
Parts of an expression coefficient variable
Parts of Expression 6abc How many factors does this expression have?
Evaluating Expressions Evaluating expressions means that you are substituting a number for your variable. For example: g-h, where g=8 and h=5 g-h = 8-5 =3 Another example : 2a+b, where a=4 b=7 2a+b = 2(4) + 7 = 8+7 =15
Adding Polynomials Add the following polynomials using column form: (4x2 – 2xy + 3y2) + (-3x2 + 2y2) (4x2 - 2xy + 3y2) + (-3x2 + 2y2) Line up your like terms 4x2 - 2xy + 3y2 + -3x2 + 2y2 x2 - 2xy + 5y2
Subtracting Polynomials Subtract the following polynomials using column form: (4x2 + 3y2) - (-10x2 +5xy - 7y2 - 9) (4x2 + 3y2) + (10x2 - 5xy + 7y2 + 9) Line up your like terms 4x2 + 3y2 + 10x2 - 5xy + 7y2 + 9 14x2 -5xy + 10y2 + 9
Subtracting Polynomials Subtract the following polynomials using column form: (3x2 – 2xy + 3y2) - (-6x2 +11xy - 7y2) (3x2 - 2xy + 3y2) + (6x2 - 11xy + 7y2) Line up your like terms 3x2 - 2xy + 3y2 + 6x2 -11xy + 7y2 9x2 -13xy + 10y2
Multiplying a polynomial by a monomial Multiply: 3x2y(2x + 4y2) To multiply we need to distribute the 3x2y over the addition. 3x2y(2x + 4y2) = (3x2y * 2x) + (3x2y* 4y2) = 6x3y + 12x2y3
Multiplying a polynomial by a polynomial (x + 3)(x – 3) x(x) + x(–3) + 3(x) + 3(–3) x2 – 3x + 3x – 9 x2 – 9
Multiplying a polynomial by a polynomial (perfect square) (x + 7)2 (x + 7)(x + 7) x(x) + x(7) + 7(x) + 7(7) x2 + 7x + 7x + 49 x2 +14x +49
Area and Perimeter A rectangle has a length of 2x2+3 and a width of x2. Write and simplify an expression for the perimeter and area of the rectangle.
Perimeter 2x2+3 x2 x2 2x2+3
Perimeter Perimeter = side + side + side + side Perimeter = 2x2+3 + x2 + 2x2+3 + x2 Perimeter = 6x2+6
Area 2x2+3 x2
Area Area = length x width Area = (x2)(2x2+3) Area = (x2)(2x2) + (x2)(3) Area = 2x4+ 3x2
Area and Perimeter A triangle has sides with lengths of 2x2+4, 4x2+y, and 2x-3y. Write and simplify an expression for the perimeter of the triangle.
Perimeter 2x2+4 4x2+y 2x-3y
Perimeter Perimeter = side + side + side Perimeter = 2x2+4 + 4x2+y + 2x-3y Perimeter = 6x2+2x – 2y + 4
Area 2x2+4x +3 Height 2x Base
Area Area = ½ (base x height) Area = ½ (2x) (2x2+4x+3) Area = ½((2x)(2x2) + (2x)(4x)+ (2x)(3)) Area = ½ (4x3+ 8x2+6x) Area = 4x3 + 8x2 + 6x 2 2 2 Area = 2x3+ 4x2+3x