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Distributive Property with Variables

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Distributive Property with Variables 2

Distributive Property with Variables 2

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Question 1 of 4

1. Question

Simplify the expression

8 p (4 q - 3 + p)

$8p(4q-3+p)$

1. $32 p q + 24 p - 8 p$ $32pq+24p-8p$
2. $32 q^{2} - 24 p q + 8 p^{2}$ $32q^2-24pq+8p^2$
3. $32 p q - 24 p + 8 p^{2}$ $32pq-24p+8p^2$
4. $32 p q + 24 q - 8 p q^{2}$ $32pq+24q-8pq^2$

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Distribute $8 p$ $8p$ to the values inside the parenthesis

		$8 p$ $8p$ $(4 q - 3 + p)$ $(4q-3+p)$
	$=$ $=$	$($ $($ $8 p$ $8p$ $\times 4 q) - ($ $xx4q)-($ $8 p$ $8p$ $\times 3) + ($ $xx3)+($ $8 p$ $8p$ $\times p)$ $xxp)$
	$=$ $=$	$[(8 \times 4) \times p \times q] - [8 \times 3 \times p] + [8 \times p \times p]$ $[(8xx4)xxpxxq]-[8xx3xxp]+[8xxpxxp]$	Keep the constants on the left side
	$=$ $=$	$[32 \times p \times q] - [24 \times p] + [8 \times p^{1 + 1}]$ $[32xxpxxq]-[24xxp]+[8xxp^(1+1)]$	Multiplication property of exponents
	$=$ $=$	$32 p q - 24 p + 8 p^{2}$ $32pq-24p+8p^2$	Combine the constant with the variable

32 p q - 24 p + 8 p^{2}

$32pq-24p+8p^2$

Question 2 of 4

2. Question

Simplify the expression

7 x y (x^{2} + 2)

$7xy(x^2+2)$

1. $7 x y^{2} - 14 x y$ $7xy^2-14xy$
2. $7 x^{3} y + 14 x y$ $7x^3y+14xy$
3. $7 x y + x^{2} + 14 x y$ $7xy+x^2+14xy$
4. $21 x^{2} y + 7 y$ $21x^2y+7y$

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

		$7 x y$ $7xy$ $(x^{2} + 2)$ $(x^2+2)$
	$=$ $=$	$($ $($ $7 x y$ $7xy$ $\times x^{2}) + ($ $xx x^2)+($ $7 x y$ $7xy$ $\times 2)$ $xx2)$
	$=$ $=$	$[7 \times (x^{2} \times x) \times y] + [(7 \times 2) \times x \times y]$ $[7xx(x^2xx x)xxy]+[(7xx2)xx x xx y]$	Keep the constants on the left side
	$=$ $=$	$[7 \times x^{2 + 1} \times y] + [14 \times x \times y]$ $[7xxx^(2+1)xxy]+[14xx x xx y]$	Multiplication property of exponents
	$=$ $=$	$7 x^{3} y + 14 x y$ $7x^3y+14xy$	Combine the constant with the variable

7 x^{3} y + 14 x y

$7x^3y+14xy$

Question 3 of 4

3. Question

Simplify the expression

3 m (5 m - n - 2)

$3m(5m-n-2)$

1. $5 m + 3 m n^{2} - 6 n$ $5m+3mn^2-6n$
2. $15 m^{2} - 3 m n - 6 m$ $15m^2-3mn-6m$
3. $12 m - 9 m^{2} n - 6 m$ $12m-9m^2n-6m$
4. $12 m + 9 m n^{2} + 6 m^{2}$ $12m+9mn^2+6m^2$

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Distribute $3 m$ $3m$ to the values inside the parenthesis

		$3 m$ $3m$ $(5 m - n - 2)$ $(5m-n-2)$
	$=$ $=$	$($ $($ $3 m$ $3m$ $\times 5 m) - ($ $xx5m)-($ $3 m$ $3m$ $\times n) - ($ $xxn)-($ $3 m$ $3m$ $\times 2)$ $xx2)$
	$=$ $=$	$[(3 \times 5) \times (m \times m)] - [3 \times m \times n] - [3 \times 2 \times m]$ $[(3xx5)xx(mxxm)]-[3xxmxxn]-[3xx2xxm]$	Keep the constants on the left side
	$=$ $=$	$[15 \times m^{1 + 1}] - [3 \times m \times n] - [6 \times m]$ $[15xxm^(1+1)]-[3xxmxxn]-[6xxm]$	Multiplication property of exponents
	$=$ $=$	$15 m^{2} - 3 m n - 6 m$ $15m^2-3mn-6m$	Remove multiplication signs

15 m^{2} - 3 m n - 6 m

$15m^2-3mn-6m$

Question 4 of 4

4. Question
Simplify the expression

$4 (3 y - 1) + 2 y$ $4(3y-1)+2y$
- (14y-4)
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Distribute $4$ $4$ to the values inside the parenthesis

$4$ $4$ $(3 y - 1) + 2 y$ $(3y-1)+2y$

$=$ $=$ $($ $($ $4$ $4$ $\times 3 y) - ($ $xx3y)-($ $4$ $4$ $\times 1) + 2 y$ $xx1)+2y$

$=$ $=$ $12 y - 4 + 2 y$ $12y-4+2y$

Simplify further by combining like terms

$12 y$ $12y$ $- 20 +$ $-20+$ $2 y$ $2y$ $=$ $=$ $($ $($ $12 y + 2 y$ $12y+2y$ $) - 4$ $)-4$

$=$ $=$ $14 y$ $14y$ $- 4$ $-4$

$14 y - 4$ $14y-4$

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Evaluate Multi Variable Expressions Involving Negative Numbers 1
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Write Algebraic Expressions from Diagrams
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