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Simplify Algebraic Expressions 1

Simplify Algebraic Expressions 1

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Question 1 of 4

1. Question
Simplify the expression

$- 5 \times y \times 2$ $-5 xx y xx 2$
- (-10y)
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When simplifying an expression, keep the constant at the left side and make sure no variables are repeated.

First, combine the constants and solve for their product

$- 5$ $-5$ $\times y \times$ $xxyxx$ $2$ $2$ $=$ $=$ $- 5 \times 2$ $-5xx2$ $\times y$ $xxy$

$=$ $=$ $- 10$ $-10$ $\times y$ $xxy$

Now that there are no repeated variables and the constant is kept at the left, we can simply remove the multiplication sign.

$- 10 \times y$ $-10xxy$ $=$ $=$ $- 10 y$ $-10y$

$- 10 y$ $-10y$
Question 2 of 4

2. Question
Simplify the expression

$a \times a \times b \times 2$ $a xx a xx b xx 2$
- 1. $2 a^{2} b$ $2a^2b$
- 2. $2 a b$ $2ab$
- 3. $2 a 2 b$ $2a2b$
- 4. $a a b^{2}$ $aab^2$
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When simplifying an expression, keep the constant at the left side and make sure no variables are repeated.

Multiplication Property of Exponents

$a^{n} \times a^{m} = a^{n + m}$ $a^nxxa^m=a^(n+m)$

First, keep the constants to the left side of the expression.

$a \times a \times b \times$ $axxaxxbxx$ $2$ $2$ $=$ $=$ $2$ $2$ $\times a \times a \times b$ $xxaxxaxxb$

Next, combine the same variables by multiplying them.

Remember that all values without exponents have $1$ $1$ as a hidden exponent.

$2 \times a^{1} \times a^{1} \times b$ $2xxa^1xxa^1xxb$ $=$ $=$ $2 \times a^{(1 + 1)} \times b$ $2xxa^((1+1))xxb$ Multiplication property of exponents

$=$ $=$ $2 \times a^{2} \times b$ $2xxa^2xxb$

Now that there are no repeated variables and the constant is kept at the left, we can simply remove the multiplication sign.

$2 \times a^{2} \times b$ $2xxa^2xxb$ $=$ $=$ $2 a^{2} b$ $2a^2b$

$2 a^{2} b$ $2a^2b$
Question 3 of 4

3. Question
Simplify the expression

$7 f \times 2 f \times 3$ $7f xx 2f xx 3$
- 1. $21 f$ $21f$
- 2. $21^{2} f$ $21^2f$
- 3. $42 f^{2}$ $42f^2$
- 4. $f 14 f$ $f14f$
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When simplifying an expression, keep the constant at the left side and make sure no variables are repeated.

Multiplication Property of Exponents

$a^{n} \times a^{m} = a^{n + m}$ $a^nxxa^m=a^(n+m)$

First, keep the constants to the left side of the expression.

$7$ $7$ $f \times$ $fxx$ $2$ $2$ $f \times$ $fxx$ $3$ $3$ $=$ $=$ $7 \times 2 \times 3$ $7xx2xx3$ $\times f \times f$ $xxfxxf$

$=$ $=$ $42$ $42$ $\times f \times f$ $xxfxxf$

Next, combine the same variables by multiplying them.

Remember that all values without exponents have $1$ $1$ as a hidden exponent.

$42 \times f^{1} \times f^{1}$ $42xxf^1xxf^1$ $=$ $=$ $42 \times f^{(1 + 1)}$ $42xxf^((1+1))$ Multiplication property of exponents

$=$ $=$ $42 \times f^{2}$ $42xxf^2$

Now that there are no repeated variables and the constant is kept at the left, we can simply remove the multiplication sign.

$42 \times f^{2}$ $42xxf^2$ $=$ $=$ $42 f^{2}$ $42f^2$

$42 f^{2}$ $42f^2$
Question 4 of 4

4. Question
Find the correct simplified expression

$5 \times (m - 3)$ $5xx(m-3)$
- 1. $5 (m - 3)$ $5(m-3)$
- 2. $15 (m)$ $15(m)$
- 3. $m (5 - 3)$ $m(5-3)$
- 4. $5 (3) m$ $5(3)m$
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When simplifying an expression, keep the constant at the left side and make sure no variables are repeated.

Multiplication Property of Exponents

$a^{n} \times a^{m} = a^{n + m}$ $a^nxxa^m=a^(n+m)$

In algebraic terms, constants and variables next together means they are being multiplied to each other.

Therefore, $5 \times (m - 3)$ $5xx(m-3)$ can be expressed as $5 (m - 3)$ $5(m-3)$ .

$5 (m - 3)$ $5(m-3)$

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