Warm-up: Write in scientific notation: ,490,000

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Presentation transcript:

Warm-up: Write in scientific notation: 0.003481 3,490,000 HW: pg.36 (4, 7, 8, 12, 21, 24, 30, 32, 34, 45, 46) pg.38 (68, 93, 94)

Objective: Operations with Algebraic Expressions Special Product Patterns Sum and difference of same terms Binomial Square Binomial Cube Factoring Greatest Common Term

Operations With Algebraic Expressions An algebraic expression of the form axn, where the coefficient a is a real number and n is a nonnegative integer, is called a monomial, meaning it consists of one term. Examples: 7x2 2xy 12x3y4 A polynomial is a monomial or the sum of two or more monomials. 4x x4 – 3 x2y – xy + y

Operations With Algebraic Expressions Constant terms, or terms containing the same variable factors are called like, or similar, terms. Like terms may be combined by adding or subtracting their numerical coefficients. Examples: 3x + 7x = 10x 12xy – 17xy = – 5xy

Examples Simplify the expression

Examples Simplify the expression

Examples Perform the operation and simplify the expression

Examples Perform the operation and simplify the expression

Special Products Let a and b be real numbers, variables, or algebraic expressions. Sum and Difference of Same Terms (a - b)(a + b) = a2 - b2 Square of a Binomial: (a + b)2 = a2 + 2ab + b2 (a – b)2 = a2 – 2ab + b2 Cube of a Binomial: (a + b)3 = a3 + 3a2b + 3ab2 + b3 (a – b)3 = a3 – 3a2b + 3ab2 – b3

FOIL Method (3x – 2)2 (3x – 2)(3x – 2)

FOIL Method FIRST (3x – 2)(3x – 2) 9x2

FOIL Method OUTER (3x – 2)(3x – 2) 9x2 - 6x

FOIL Method INNER (3x – 2)(3x – 2) - 6x 9x2 - 6x

FOIL Method LAST (3x – 2)(3x – 2) 9x2 - 6x - 6x + 4

FOIL Method Combine like terms (3x – 2)(3x – 2) 9x2 - 6x - 6x +4 9x2 – 12x + 4

Multiply: (3x – 2y)3 using (a – b)3 = a3 – 3a2b + 3ab2 – b3 a = 3x and b = 2y Plug into the formula a3 – 3a2b + 3ab2 – b3 (3x)3 – 3(3x)2(2y) + 3(3x)(2y)2 – (2y)3 Simplify 27x3 – 54x2y + 36xy2 – 8y3

The Product of Two Trinomials Multiply: (x + y – 2)(x + y + 2) =x2 + 2xy + y2 – 4

Factoring Factoring is the process of expressing an algebraic expression as a product of other algebraic expressions. Example:

Factoring To factor an algebraic expression, first check to see if it contains any common terms. If so, factor out the greatest common term. For example, the greatest common factor for the expression is 2a, because

Examples Factor out the greatest common factor in each expression

Factor by Grouping Factor out the greatest common factor in each group

Sneedlegrit: Multiply (2x – 4)3 Summary: Operations with Algebraic Expressions Special Product Patterns Sum and difference of same terms Binomial Square Binomial Cube Factoring Greatest Common Term Sneedlegrit: Multiply (2x – 4)3 HW: pg.36 (4, 7, 8, 12, 21, 24, 30, 32, 34, 45, 46) pg.38 (68, 93, 94)