Distributive Property with Variables 3

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Question 1 of 4

Simplify the expression

5 b (7 b - 3) - 12 b

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

1. $35 b^{2} - 27 b$ $35b^2-27b$
2. $35 b^{2} + 27 b$ $35b^2+27b$
3. $35 b + 27 b^{2}$ $35b+27b^2$
4. $35 b - 27 b^{2}$ $35b-27b^2$

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Distribute $5 b$ $5b$ to the values inside the parenthesis

	$5 b$ $5b$ $(7 b - 3) - 12 b$ $(7b-3)-12b$
$=$ $=$	$($ $($ $5 b$ $5b$ $\times 7 b) - ($ $xx7b)-($ $5 b$ $5b$ $\times 3) - 12 b$ $xx3)-12b$
$=$ $=$	$(35 \times b^{1 + 1}) - (15 \times b) - 12 b$ $(35xxb^(1+1))-(15xxb)-12b$	Multiplication property of exponents
$=$ $=$	$35 b^{2} - 15 b - 12 b$ $35b^2-15b-12b$

Simplify further by combining like terms

35 b^{2}

$35b^2$ $- 15 b - 12 b$ $-15b-12b$

=

$=$

35 b^{2}

$35b^2$ $- 27 b$ $-27b$

35 b^{2} - 27 b

$35b^2-27b$

Question 2 of 4

2. Question
Simplify the expression

$4 (2 x^{2} + 3 x + 5) - 3 x$ $4(2x^2+3x+5)-3x$
- 1. $4 x^{2} + 20 x$ $4x^2+20x$
- 2. $9 x^{2} + 8 x + 10$ $9x^2+8x+10$
- 3. $8 x^{2} + 9 x + 20$ $8x^2+9x+20$
- 4. $6 x^{2} + 3 x + 15$ $6x^2+3x+15$
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Distribute $4$ $4$ to the values inside the parenthesis

$4$ $4$ $(2 x^{2} + 3 x + 5) - 3 x$ $(2x^2+3x+5)-3x$

$=$ $=$ $($ $($ $4$ $4$ $\times 2 x^{2}) + ($ $xx2x^2)+($ $4$ $4$ $\times 3 x) + ($ $xx3x)+($ $4$ $4$ $\times 5) - 3 x$ $xx5)-3x$

$=$ $=$ $8 x^{2} + 12 x + 20 - 3 x$ $8x^2+12x+20-3x$

Simplify further by combining like terms

$8 x^{2} +$ $8x^2+$ $12 x$ $12x$ $+ 20 -$ $+20-$ $3 x$ $3x$ $=$ $=$ $8 x^{2} + ($ $8x^2+($ $12 x - 3 x$ $12x-3x$ $) + 20$ $)+20$

$=$ $=$ $8 x^{2}$ $8x^2$ $+ 9 x$ $+9x$ $+ 20$ $+20$

$8 x^{2} + 9 x + 20$ $8x^2+9x+20$

Question 3 of 4

Simplify the expression

2 (6 y^{2} - 7 y - 9) - 10 y

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

1. $12 y^{2} + 30 y - 24$ $12y^2+30y-24$
2. $12 y^{2} - 24 y - 18$ $12y^2-24y-18$
3. $12 y - 24 y + 30$ $12y-24y+30$
4. $12 y^{2} + 24 y + 18$ $12y^2+24y+18$

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Distribute $2$ $2$ to the values inside the parenthesis

		$2$ $2$ $(6 y^{2} - 7 y - 9) - 10 y$ $(6y^2-7y-9)-10y$
	$=$ $=$	$($ $($ $2$ $2$ $\times 6 y^{2}) - ($ $xx6y^2)-($ $2$ $2$ $\times 7 y) - ($ $xx7y)-($ $2$ $2$ $\times 9) - 10 y$ $xx9)-10y$
	$=$ $=$	$12 y^{2} - 14 y - 18 - 10 y$ $12y^2-14y-18-10y$

Simplify further by combining like terms

$12 y^{2} -$ $12y^2-$ $14 y$ $14y$ $- 18 -$ $-18-$ $10 y$ $10y$	$=$ $=$	$12 y^{2}$ $12y^2$ $- 14 y - 10 y$ $-14y-10y$ $- 18$ $-18$
	$=$ $=$	$12 y^{2} - 24 y - 18$ $12y^2-24y-18$

12 y^{2} - 24 y - 18

$12y^2-24y-18$

Question 4 of 4

4. Question
Simplify the expression

$3 (4 x^{2} + 1) - 2 (x^{2} + 5)$ $3(4x^2+1)-2(x^2+5)$
- 1. $10 x^{2} + 7 x$ $10x^2+7x$
- 2. $14 x^{2} + 17$ $14x^2+17$
- 3. $10 x^{2} - 7$ $10x^2-7$
- 4. $10 x + 7$ $10x+7$
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First, distribute $3$ $3$ to the values inside the left parenthesis

$3$ $3$ $(4 x^{2} + 1) - 2 (x^{2} + 5)$ $(4x^2+1)-2(x^2+5)$

$=$ $=$ $($ $($ $3$ $3$ $\times 4 x^{2}) + ($ $xx4x^2)+($ $3$ $3$ $\times 1) - 2 (x^{2} + 5)$ $xx1)-2(x^2+5)$

$=$ $=$ $12 x^{2} + 3 - 2 (x^{2} + 5)$ $12x^2+3-2(x^2+5)$

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

$12 x^{2} + 3$ $12x^2+3$ $- 2$ $-2$ $(x^{2} + 5)$ $(x^2+5)$

$=$ $=$ $12 x^{2} + 3 + ($ $12x^2+3+($ $- 2$ $-2$ $\times x^{2}) + ($ $xxx^2)+($ $- 2$ $-2$ $\times 5)$ $xx5)$

$=$ $=$ $12 x^{2} + 3 - 2 x^{2} - 10$ $12x^2+3-2x^2-10$

Simplify further by combining like terms

$12 x^{2}$ $12x^2$ $+$ $+$ $3$ $3$ $-$ $-$ $2 x^{2}$ $2x^2$ $-$ $-$ $10$ $10$ $=$ $=$ $($ $($ $12 x^{2} - 2 x^{2}$ $12x^2-2x^2$ $) + ($ $)+($ $3 - 10$ $3-10$ $)$ $)$

$=$ $=$ $10 x^{2}$ $10x^2$ $- 7$ $-7$

$10 x^{2} - 7$ $10x^2-7$

Distributive Property with Variables 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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Great Work!

4. Question

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Quizzes

		$4$ $4$ $(2 x^{2} + 3 x + 5) - 3 x$ $(2x^2+3x+5)-3x$
	$=$ $=$	$($ $($ $4$ $4$ $\times 2 x^{2}) + ($ $xx2x^2)+($ $4$ $4$ $\times 3 x) + ($ $xx3x)+($ $4$ $4$ $\times 5) - 3 x$ $xx5)-3x$
	$=$ $=$	$8 x^{2} + 12 x + 20 - 3 x$ $8x^2+12x+20-3x$

$8 x^{2} +$ $8x^2+$ $12 x$ $12x$ $+ 20 -$ $+20-$ $3 x$ $3x$	$=$ $=$	$8 x^{2} + ($ $8x^2+($ $12 x - 3 x$ $12x-3x$ $) + 20$ $)+20$
	$=$ $=$	$8 x^{2}$ $8x^2$ $+ 9 x$ $+9x$ $+ 20$ $+20$

		$3$ $3$ $(4 x^{2} + 1) - 2 (x^{2} + 5)$ $(4x^2+1)-2(x^2+5)$
	$=$ $=$	$($ $($ $3$ $3$ $\times 4 x^{2}) + ($ $xx4x^2)+($ $3$ $3$ $\times 1) - 2 (x^{2} + 5)$ $xx1)-2(x^2+5)$
	$=$ $=$	$12 x^{2} + 3 - 2 (x^{2} + 5)$ $12x^2+3-2(x^2+5)$

		$12 x^{2} + 3$ $12x^2+3$ $- 2$ $-2$ $(x^{2} + 5)$ $(x^2+5)$
	$=$ $=$	$12 x^{2} + 3 + ($ $12x^2+3+($ $- 2$ $-2$ $\times x^{2}) + ($ $xxx^2)+($ $- 2$ $-2$ $\times 5)$ $xx5)$
	$=$ $=$	$12 x^{2} + 3 - 2 x^{2} - 10$ $12x^2+3-2x^2-10$

$12 x^{2}$ $12x^2$ $+$ $+$ $3$ $3$ $-$ $-$ $2 x^{2}$ $2x^2$ $-$ $-$ $10$ $10$	$=$ $=$	$($ $($ $12 x^{2} - 2 x^{2}$ $12x^2-2x^2$ $) + ($ $)+($ $3 - 10$ $3-10$ $)$ $)$
	$=$ $=$	$10 x^{2}$ $10x^2$ $- 7$ $-7$