About Multiplying Polynomials:
When we multiply two polynomials together, we use our associative, commutative, and distributive properties, along with our rules for exponents. To multiply two binomials together quickly, we use a shortcut known as FOIL. Lastly, when we multiply more than two polynomials, we find the product of any two first and continue multiplying until we have our product.
Test Objectives
- Demonstrate the ability to find the product of two polynomials
- Demonstrate the ability to find the product of two binomials using FOIL
- Demonstrate the ability to find the product of more than two polynomials
#1:
Instructions: Find each product.
a) $$4n(6n^2 + 8n - 3)$$
b) $$(2x - 5y)(3x + 3y)$$
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#2:
Instructions: Find each product.
a) $$(6n - 4)(5n + 6)$$
b) $$(x - 4y)(2x - 3y)$$
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#3:
Instructions: Find each product.
a) $$(10x - 7)(2x^2 - 2x - 3)$$
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#4:
Instructions: Find each product.
a) $$(14x^2 - 14x - 4)(10x^2 - 6x - 9)$$
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#5:
Instructions: Find each product.
a) $$(4a - b)(5a + 3b)(a^2 - 2b + 7ab)$$
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Written Solutions:
#1:
Solutions:
a) $$24n^3 + 32n^2 - 12n$$
b) $$6x^2 - 9xy - 15y^2$$
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#2:
Solutions:
a) $$30n^2 + 16n - 24$$
b) $$2x^2 - 11xy + 12y^2$$
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#3:
Solutions:
a) $$20x^3 - 34x^2 - 16x + 21$$
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#4:
Solutions:
a) $$140x^4 - 224x^3 - 82x^2 + 150x + 36$$
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#5:
Solutions:
a) $$20a^4 - 40a^2b + 147a^3b - 14ab^2 + 46a^2b^2 + 6b^3 - 21ab^3$$
