FOIL Method – 3 Terms

Question 1 of 4

Expand and simplify.

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

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

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

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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.

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

x^{3} + 5 x^{2} + 11 x + 7

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

Question 2 of 4

Expand and simplify.

(a + 3) (a^{2} - 3 a + 9)

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

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

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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.

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

a^{3} + 27

$a^3+27$

Question 3 of 4

Expand and simplify.

(6 x - 5) (4 x^{2} + 2 x + 1)

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

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

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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.

(6 x) (4 x^{2}) + (6 x) (2 x) + (6 x) (1) + (- 5) (4 x^{2}) + (- 5) (2 x) + (- 5) (1)

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

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

24 x^{3} - 8 x^{2} - 4 x - 5

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

Question 4 of 4

Expand and simplify.

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

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

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

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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
$=$ $=$	$(x + 1) (x^{2} + 8 x + 15)$ $(x+1)(x^2+8x+15)$

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.

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

x^{3} + 9 x^{2} + 23 x + 15

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

FOIL Method – 3 Terms

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