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PSAT Math : How to use FOIL in the distributive property

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Example Question #11 : How To Use Foil In The Distributive Property

If $\displaystyle f(x) = 3x-2$, $\displaystyle g(x) = 2x+3$, and $h(x) = f(x) \times g(x)$ $\displaystyle h(x) = f(x) \times g(x)$, then h(x) =? $\displaystyle h(x) =?$

Possible Answers:

6x-1 $\displaystyle 6x-1$

$6x^{2}-4x-6$ $\displaystyle 6x^{2}-4x-6$

$6x^{2} + 9x +6$ $\displaystyle 6x^{2} + 9x +6$

6x-6 $\displaystyle 6x-6$

$6x^{2} +5x-6$ $\displaystyle 6x^{2} +5x-6$

Correct answer:

$6x^{2} +5x-6$ $\displaystyle 6x^{2} +5x-6$

Explanation:

To find what h(x) $\displaystyle h(x)$ equals, you must know how to multiply f(x) $\displaystyle f(x)$ times g(x) $\displaystyle g(x)$, or, you must know how to multiply binomials. The best way to multiply monomials is the FOIL (first, outside, inside, last) method, as shown below:

$h(x) = f(x)\times g(x) = (3x-2)\times (2x+3)$ $\displaystyle h(x) = f(x)\times g(x) = (3x-2)\times (2x+3)$

Multiply the First terms

$3x\cdot 2x= 6x^{2}$ $\displaystyle 3x\cdot 2x= 6x^{2}$

Multiply the Outside terms:

$3x\cdot3 = 9x$ $\displaystyle 3x\cdot3 = 9x$

Multiply the Inside terms:

$-2\cdot2x = -4x$ $\displaystyle -2\cdot2x = -4x$

Note: this step yields a negative number because the product of the two terms is negative.

Multiply the Last terms:

$-2\cdot3=-6$ $\displaystyle -2\cdot3=-6$

Note: this step yields a negative number too!

Putting the results together, you get:

$(3x-2)\times (2x+3) = 6x^{2} +9x-4x -6$ $\displaystyle (3x-2)\times (2x+3) = 6x^{2} +9x-4x -6$

Finally, combine like terms, and you get:

$h(x) = 6x^{2} +5x-6$ $\displaystyle h(x) = 6x^{2} +5x-6$

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PSAT Math : How to use FOIL in the distributive property

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Example Question #11 : How To Use Foil In The Distributive Property

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