Quick Review 2-2

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Unit 2 - Objective 2 - Multiplying Polynomials

You may need to review Unit 1 - Objective 4 - Rules of Exponents again. Remember a^m · aⁿ = a^{m + n}.

Examples:

1.	(3x³) (- 7bx⁴) = - 21bx^{3 + 4} = - 21bx⁷
2.	(- 5xy²z³) (3x²y²) = -15x^{1 + 2}y^{2 + 2}z³ = -15x³y⁴z³

If a mononomial is raised to a power, first raise it to the indicated power before multiplying the rest of the problem.

Examples:

1.	5 (2x²y³)²	=	5 (2² (x²)² (y³)²)
		=	5 (4x⁴y⁶)
		=	20x⁴y⁶

2.	2a³ (-ab⁴)² (4a²b)	=	2a³ ((-a)² (b⁴)²) (4a²b)
		=	2a³ (a²b⁸) (4a²b)
		=	(2) (4) a^{3 + 2} ^{+ 2} b^{8 + 1}
		=	8a⁷b⁹

To find the product of a mononomial and a polynomial use the distributive law.

Examples:

1.	4x²y (3xy² + 2x³y)
		= (4x²y) (3xy²) + (4x²y) (2x³y)
		= 12x^{2 + 1}y^{1 + 2} + 8x^{2 + 3}y^{1 + 1}
		= 12x³y³ + 8x⁵y²

2.	- 7ab² (2ax³ - 5abx + 3b³)
		= (-7ab²) (2ax³) + (- 7ab²) (- 5abx) + (-7ab²) (3b³)
		= -14a^{1 + 1}b²x³ +35a^{1 + 1}b^{2 + 1}x - 21ab^{2 + 3}
		= -14a²b²x³ + 35a²b³x - 21ab⁵

To multiply polynomials use the distributive law and the laws of exponents. Remember the FOIL Method when multiplying two binomials which is Multiply First terms, Outside terms, Inside terms, Last terms.

Examples:

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NOTE: (The second line of #2 - I forgot the term +(-3c)(a²))