Simplify Algebraic Expressions using the Distributive Property 3

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Question 1 of 4

Simplify the expression

5 b (7 b - 3) - 12 b

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

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

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. $6 x^{2} + 3 x + 15$ $6x^2+3x+15$
- 3. $9x^2+8x+10$
- 4. $8x^2+9x+20$
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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

$2(6y^2-7y-9)-10y$
- 1. $12y^2-24y-18$
- 2. $12y^2+30y-24$
- 3. $12y-24y+30$
- 4. $12y^2+24y+18$
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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

$3(4x^2+1)-2(x^2+5)$
- 1. $10x+7$
- 2. $14x^2+17$
- 3. $10x^2+7x$
- 4. $10x^2-7$
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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

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

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

$10x^2-7$

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

Simplify Algebraic Expressions using the Distributive Property 3

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Quizzes

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

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

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

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

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

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

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