multiply polynomials when multiplying polynomials, we always use the distributive property
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Multiply Polynomials
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When multiplying polynomials, we always use When multiplying polynomials, we always use the the Distributive PropertyDistributive Property. .
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-x(4x2 + x - 8) + 7(4x2 + x - 8).-4x3 – x2 + 8x + 28x2 + 7x - 56
Combine like terms.-4x3 + 27x2 + 15x - 56
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x(-4x2 + 5x - 2) - 3(-4x2 + 5x - 2).
-4x3 + 5x2 - 2x + 12x2 - 15x + 6Combine like terms.
-4x3 + 17x2 - 17x + 6
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A SHORTCUTSHORTCUT of the distributive property is called the FOIL
method.
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6x2
F O I LFirst
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F O I LFirst
6x2 - 8x
Outer
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F O I LFirst Outer Inner
6x2 - 8x + 3x
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Combine like terms.
6x2 - 5x - 4
F O I LFirst
6x2 - 8x + 3x - 4
Outer Inner Last
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First terms
Outer terms
Inner terms
Last terms
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F O I L
5x(3x) + 5x(-2) + 2(3x) + 2(-2).15x2 – 10x + 6x - 4Combine like terms.
15x2 – 4x - 4
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F O I L
2x2 + 7x – 8x – 28Combine like terms.
2x2 – x – 28
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F O I L
2x2 – 18x + 3x – 27Combine like terms.
2x2 – 15x – 27
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(x + 3) (2x – 7)= 2x2 – 7x + 6x – 21Combine like terms.
2x2 - x - 21
(x + 3)
(2x - 7)(2x-7)
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Write a polynomial that represents the area of the shaded region:
(x + 3)
(2x - 7)(x+6)