Distributive Property with Variables 1

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Question 1 of 5

1. Question
Simplify the expression

$3 (a + 4)$ $3(a+4)$
- (3a+12)
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Distribute $3$ $3$ to the values inside the parenthesis

$3$ $3$ $(a + 4)$ $(a+4)$

$=$ $=$ $($ $($ $3$ $3$ $\times a) + ($ $xxa)+($ $3$ $3$ $\times 4)$ $xx4)$

$=$ $=$ $3 a + (3 \times 4)$ $3a+(3xx4)$ Combine the constant with the variable

$=$ $=$ $3 a + 12$ $3a+12$ Simplify further

$3 a + 12$ $3a+12$

Question 2 of 5

Simplify the expression

x (2 x - 5)

$x(2x-5)$

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

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Distribute $x$ $x$ to the values inside the parenthesis

	$x$ $x$ $(2 x - 5)$ $(2x-5)$
$=$ $=$	$(2 x \times$ $(2x xx$ $x$ $x$ $) - (5 \times$ $)-(5xx$ $x$ $x$ $)$ $)$
$=$ $=$	$(2 x^{1 + 1}) - (5 \times x)$ $(2x^(1+1))-(5xxx)$	Multiplication property of exponents
$=$ $=$	$2 x^{2} - 5 x$ $2x^2-5x$	Combine the constant with the variable

2 x^{2} - 5 x

$2x^2-5x$

Question 3 of 5

Simplify the expression

(5 - 8 x) 11

$(5-8x)11$

(55-88x)

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

	$(5 - 8 x)$ $(5-8x)$ $11$ $11$
$=$ $=$	$(5 \times$ $(5xx$ $11$ $11$ $) - (8 x \times$ $)-(8x xx$ $11$ $11$ $)$ $)$
$=$ $=$	$55 - (8 \times 11 \times x)$ $55-(8xx11xx x)$	Keep constants to the left side
$=$ $=$	$55 - 88 x$ $55-88x$	Combine the constant with the variable

55 - 88 x

$55-88x$

Question 4 of 5

Simplify the expression

7 y (6 - 3 y)

$7y(6-3y)$

1. $42 y + 21 y$ $42y+21y$
2. $40 y + 24 y^{2}$ $40y+24y^2$
3. $14 y^{2} - 20 y$ $14y^2-20y$
4. $42 y - 21 y^{2}$ $42y-21y^2$

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Distribute $7 y$ $7y$ to the values inside the parenthesis

	$7 y$ $7y$ $(6 - 3 y)$ $(6-3y)$
$=$ $=$	$($ $($ $7 y$ $7y$ $\times 6) - ($ $xx6)-($ $7 y$ $7y$ $\times 3 y)$ $xx3y)$
$=$ $=$	$[7 \times 6 \times y] - [(7 \times 3) \times (y \times y)]$ $[7xx6xxy]-[(7xx3)xx(yxxy)]$	Keep the constants on the left side
$=$ $=$	$[42 \times y] - [21 \times y^{1 + 1}]$ $[42xxy]-[21xxy^(1+1)]$	Multiplication property of exponents
$=$ $=$	$42 y - 21 y^{2}$ $42y-21y^2$	Combine the constant with the variable

42 y - 21 y^{2}

$42y-21y^2$

Question 5 of 5

Simplify the expression

3 a b (2 a + b)

$3ab(2a+b)$

1. $3 a b + 3 a^{2} b^{2}$ $3ab+3a^2b^2$
2. $2 a b^{2} + 3 a b$ $2ab^2+3ab$
3. $6 a b^{2} + 6 a b$ $6ab^2+6ab$
4. $6 a^{2} b + 3 a b^{2}$ $6a^2b+3ab^2$

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Distribute $3 a b$ $3ab$ to the values inside the parenthesis

	$3 a b$ $3ab$ $(2 a + b)$ $(2a+b)$
$=$ $=$	$($ $($ $3 a b$ $3ab$ $\times 2 a) + ($ $xx2a)+($ $3 a b$ $3ab$ $\times b)$ $xxb)$
$=$ $=$	$[(3 \times 2) \times (a \times a) \times b] + [3 a \times (b \times b)]$ $[(3xx2)xx(axxa)xxb]+[3axx(bxxb)]$	Keep the constants on the left side
$=$ $=$	$[(6) \times a^{1 + 1} \times b] + [3 a \times b^{1 + 1}]$ $[(6)xxa^(1+1)xxb]+[3axxb^(1+1)]$	Multiplication property of exponents
$=$ $=$	$6 a^{2} b + 3 a b^{2}$ $6a^2b+3ab^2$	Combine the constant with the variable

6 a^{2} b + 3 a b^{2}

$6a^2b+3ab^2$

Distributive Property with Variables 1

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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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5. Question

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Quizzes

	$3$ $3$ $(a + 4)$ $(a+4)$
$=$ $=$	$($ $($ $3$ $3$ $\times a) + ($ $xxa)+($ $3$ $3$ $\times 4)$ $xx4)$
$=$ $=$	$3 a + (3 \times 4)$ $3a+(3xx4)$	Combine the constant with the variable
$=$ $=$	$3 a + 12$ $3a+12$	Simplify further