FOIL Method – 3 Terms

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Question 1 of 4

Expand and simplify.

(x + 1) (x^{2} + 4 x + 7)

$(x+1)(x^2+4x+7)$

1. $x^3+5x^2+11x+7$
2. $x^3+4x^2+7x+5$
3. $x^3+2x^2+8x+4$
4. $x^3+11x^2+2x+5$

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Use FOIL Method – 3 Terms to expand and simplify the expression.

Multiply all the terms of the trinomial to the First and Last term of the binomial, then simplify.

	$(\color{#D800AD}{x})(x^2)+(\color{#D800AD}{x})(4x)+(\color{#D800AD}{x})(7)+(\color{#9E8600}{1})(x^2)+(\color{#9E8600}{1})(4x)+(\color{#9E8600}{1})(7)$
$=$	$x^3+4x^2+7x+x^2+4x+7$
$=$	$x^3+(4x^2+x^2)+(7x+4x)+7$	Collect like terms
$=$	$x^3+5x^2+11x+7$

$x^3+5x^2+11x+7$

Question 2 of 4

Expand and simplify.

$(a+3)(a^2-3a+9)$

1. $a^3+27$
2. $a^3-9a+27$
3. $a^3-3a^2-9a+27$
4. $a^3+3a^2-27$

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Use FOIL Method – 3 Terms to expand and simplify the expression.

Multiply all the terms of the trinomial to the First and Last term of the binomial, then simplify.

	$(\color{#D800AD}{a})(a^2)+(\color{#D800AD}{a})(-3a)+(\color{#D800AD}{a})(9)+(\color{#9E8600}{3})(a^2)+(\color{#9E8600}{3})(-3a)+(\color{#9E8600}{3})(9)$
$=$	$a^3-3a^2+9a+3a^2-9a+27$
$=$	$a^3+(-3a^2+3a^2)+(9a-9a)+27$	Collect like terms
$=$	$a^3+0+0+27$
$=$	$a^3+27$

$a^3+27$

Question 3 of 4

Expand and simplify.

$(6x-5)(4x^2+2x+1)$

1. $24x^3+12x^2+16x-5$
2. $24x^3-12x^2+16x-5$
3. $24x^3+8x^2-4x-5$
4. $24x^3-8x^2-4x-5$

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Use FOIL Method – 3 Terms to expand and simplify the expression.

Multiply all the terms of the trinomial to the First and Last term of the binomial, then simplify.

$(\color{#D800AD}{6x})(4x^2)+(\color{#D800AD}{6x})(2x)+(\color{#D800AD}{6x})(1)+(\color{#9E8600}{-5})(4x^2)+(\color{#9E8600}{-5})(2x)+(\color{#9E8600}{-5})(1)$

$=$	$24x^3+12x^2+6x-20x^2-10x-5$
$=$	$24x^3$ $+12x^2$ $+6x$ $-20x^2$ $-10x-5$	Collect like terms
$=$	$24x^3-8x^2$ $+6x-10x$ $-5$	Collect like terms
$=$	$24x^3-8x^2-4x-5$

$24x^3-8x^2-4x-5$

Question 4 of 4

Expand and simplify.

$(x+1)(x+3)(x+5)$

1. $2x^3+7x^2+7x+8$
2. $x^3+9x^2+23x+15$
3. $x^3+23x^2+9x+4$
4. $3x^3+2x^2+27x+10$

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First, use the FOIL Method to expand and simplify the expressions inside the second and third brackets.

Multiply the First, Outside, Inside, and Last terms, then simplify.

	$\color{#9E9E9E}{(x+1)}[\color{#00880A}{(x)(x)}+\color{#9a00c7}{(x)(5)}+\color{#007DDC}{(3)(x)}+\color{#e65021}{(3)(5)}]$
$=$	$\color{#9E9E9E}{(x+1)}(x^2+5x+3x+15)$
$=$	$\color{#9E9E9E}{(x+1)}(x^2\color{#CC0000}{+5x+3x}+15)$	Collect like terms
$=$	$(x+1)(x^2+8x+15)$

Finally, use FOIL Method – 3 Terms to expand and simplify the remaining values.

Multiply all the terms of the trinomial to the First and Last term of the binomial, then simplify.

	$(\color{#D800AD}{x})(x^2)+(\color{#D800AD}{x})(8x)+(\color{#D800AD}{x})(15)+(\color{#9E8600}{1})(x^2)+(\color{#9E8600}{1})(8x)+(\color{#9E8600}{1})(15)$
$=$	$x^3+8x^2+15x+x^2+8x+15$
$=$	$x^3$ $+8x^2$ $+15x$ $+x^2$ $+8x+15$	Collect like terms
$=$	$24x^3+9x^2$ $+15x+8x$ $+15$	Collect like terms
$=$	$x^3+9x^2+23x+15$

$x^3+9x^2+23x+15$

FOIL Method – 3 Terms

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