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Multiply Polynomials

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When multiplying polynomials, we always use the Distributive Property.

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-x (4x 2 + x - 8) + 7 (4x 2 + x - 8). -4x 3 – x 2 + 8x + 28x 2 + 7x - 56 Combine like terms. -4x 3 + 27x 2 + 15x - 56

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x (-4x 2 + 5x - 2) - 3 (-4x 2 + 5x - 2). -4x 3 + 5x 2 - 2x + 12x 2 - 15x + 6 Combine like terms. -4x 3 + 17x 2 - 17x + 6

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SHORTCUT A SHORTCUT of the distributive property is called the FOIL method.

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6x 2 FOIL First

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FOIL 6x 2 - 8x Outer

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FOIL First Outer Inner 6x 2 - 8x + 3x

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Combine like terms. 6x 2 - 5x - 4 FOIL First 6x 2 - 8x + 3x - 4 Outer Inner Last

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F irst terms O uter terms I nner terms L ast terms

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F O I L 5x(3x) + 5x(-2) + 2(3x) + 2(-2). 15x 2 – 10x + 6x - 4 Combine like terms. 15x 2 – 4x - 4

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F O I L 2x 2 + 7x – 8x – 28 Combine like terms. 2x 2 – x – 28

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F O I L 2x 2 – 18x + 3x – 27 Combine like terms. 2x 2 – 15x – 27

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(x + 3) (2x – 7) = 2x 2 – 7x + 6x – 21 Combine like terms. 2x 2 - x - 21 (2x-7)

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Write a polynomial that represents the area of the shaded region: (x+6)

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