FOIL Method – 3 Terms | VividMath

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Question 1 of 4

Expand and simplify.

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

Question 2 of 4

Expand and simplify.

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

Question 4 of 4

Expand and simplify.

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

FOIL Method – 3 Terms

	$$(\color{#D800AD}{x})(x^2)+(\color{#D800AD}{x})(4x)+(\color{#D800AD}{x})(7)+(\color{#9E8600}{1})(x^2)+(\color{#9E8600}{1})(4x)+(\color{#9E8600}{1})(7)$$
`=`	`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`

	$$(\color{#D800AD}{a})(a^2)+(\color{#D800AD}{a})(-3a)+(\color{#D800AD}{a})(9)+(\color{#9E8600}{3})(a^2)+(\color{#9E8600}{3})(-3a)+(\color{#9E8600}{3})(9)$$
`=`	`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`

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

	$$(\color{#D800AD}{x})(x^2)+(\color{#D800AD}{x})(8x)+(\color{#D800AD}{x})(15)+(\color{#9E8600}{1})(x^2)+(\color{#9E8600}{1})(8x)+(\color{#9E8600}{1})(15)$$
`=`	`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`