Simplify Algebraic Expressions using the Distributive Property 3

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Question 1 of 4

1. Question
Simplify the expression

`5b(7b-3)-12b`
- `35b^2-27b`
- `35b^2+27b`
- `35b-27b^2`
- `35b+27b^2`
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Correct

Well Done!

Incorrect

Distribute `5b` to the values inside the parenthesis

`5b``(7b-3)-12b`

`=` `(``5b``xx7b)-(``5b``xx3)-12b`

`=` `(35xxb^(1+1))-(15xxb)-12b` Multiplication property of exponents

`=` `35b^2-15b-12b`

Simplify further by combining like terms

`35b^2``-15b-12b` `=` `35b^2``-27b`

`35b^2-27b`
Question 2 of 4

2. Question
Simplify the expression

`4(2x^2+3x+5)-3x`
- `8x^2+9x+20`
- `9x^2+8x+10`
- `6x^2+3x+15`
- `4x^2+20x`
Hint

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Correct

Nice Job!

Incorrect

Distribute `4` to the values inside the parenthesis

`4``(2x^2+3x+5)-3x`

`=` `(``4``xx2x^2)+(``4``xx3x)+(``4``xx5)-3x`

`=` `8x^2+12x+20-3x`

Simplify further by combining like terms

`8x^2+``12x` `+20-``3x` `=` `8x^2+(``12x-3x``)+20`

`=` `8x^2``+9x` `+20`

`8x^2+9x+20`
Question 3 of 4

3. Question
Simplify the expression

`2(6y^2-7y-9)-10y`
- `12y^2-24y-18`
- `12y^2+30y-24`
- `12y-24y+30`
- `12y^2+24y+18`
Hint

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Correct

Great Work!

Incorrect

Distribute `2` to the values inside the parenthesis

`2``(6y^2-7y-9)-10y`

`=` `(``2``xx6y^2)-(``2``xx7y)-(``2``xx9)-10y`

`=` `12y^2-14y-18-10y`

Simplify further by combining like terms

`12y^2-``14y` `-18-``10y` `=` `12y^2` `-14y-10y` `-18`

`=` `12y^2-24y-18`

`12y^2-24y-18`
Question 4 of 4

4. Question
Simplify the expression

`3(4x^2+1)-2(x^2+5)`
- `10x^2-7`
- `14x^2+17`
- `10x+7`
- `10x^2+7x`
Hint

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Correct

Fantastic!

Incorrect

First, distribute `3` to the values inside the left parenthesis

`3``(4x^2+1)-2(x^2+5)`

`=` `(``3``xx4x^2)+(``3``xx1)-2(x^2+5)`

`=` `12x^2+3-2(x^2+5)`

Next, distribute `-2` to the values inside the right parenthesis

`12x^2+3``-2``(x^2+5)`

`=` `12x^2+3+(``-2``xxx^2)+(``-2``xx5)`

`=` `12x^2+3-2x^2-10`

Simplify further by combining like terms

`12x^2``+``3``-``2x^2``-``10` `=` `(``12x^2-2x^2``)+(``3-10``)`

`=` `10x^2` `-7`

`10x^2-7`

Simplify Algebraic Expressions using the Distributive Property 3

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Quiz summary

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1. Question

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2. Question

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3. Question

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4. Question

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Quizzes

	`5b``(7b-3)-12b`
`=`	`(``5b``xx7b)-(``5b``xx3)-12b`
`=`	`(35xxb^(1+1))-(15xxb)-12b`	Multiplication property of exponents
`=`	`35b^2-15b-12b`

		`4``(2x^2+3x+5)-3x`
	`=`	`(``4``xx2x^2)+(``4``xx3x)+(``4``xx5)-3x`
	`=`	`8x^2+12x+20-3x`

`8x^2+``12x` `+20-``3x`	`=`	`8x^2+(``12x-3x``)+20`
	`=`	`8x^2``+9x` `+20`

		`2``(6y^2-7y-9)-10y`
	`=`	`(``2``xx6y^2)-(``2``xx7y)-(``2``xx9)-10y`
	`=`	`12y^2-14y-18-10y`

`12y^2-``14y` `-18-``10y`	`=`	`12y^2` `-14y-10y` `-18`
	`=`	`12y^2-24y-18`

		`3``(4x^2+1)-2(x^2+5)`
	`=`	`(``3``xx4x^2)+(``3``xx1)-2(x^2+5)`
	`=`	`12x^2+3-2(x^2+5)`

		`12x^2+3``-2``(x^2+5)`
	`=`	`12x^2+3+(``-2``xxx^2)+(``-2``xx5)`
	`=`	`12x^2+3-2x^2-10`

`12x^2``+``3``-``2x^2``-``10`	`=`	`(``12x^2-2x^2``)+(``3-10``)`
	`=`	`10x^2` `-7`