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QUESTION a \( 28 a b= \) c \( 7 x y= \) e \( 9 a b c= \) g \( 2 x y z= \) 1. \( 14 m n p= \) \( \qquad \) k. 5 ace \( = \) \( \qquad \) m \( 16 x= \) Write the following expressions in expanded form. b \( 8 a b c= \) d \( 7 m n= \) f \( 18 m^{2}= \) h \( 9 a^{2} b= \) j \( 8 a^{3}= \) 1 \( 17 a^{2} b^{2}= \) n \( 28 x^{2} y^{3}= \)

Ask by Love Rose. in Australia
Mar 22,2025

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Answer

Here are the expressions written in expanded form: a. \(28ab = 28 \times a \times b\) c. \(7xy = 7 \times x \times y\) e. \(9abc = 9 \times a \times b \times c\) g. \(2xyz = 2 \times x \times y \times z\) 1. \(14mnp = 14 \times m \times n \times p\) k. \(5ace = 5 \times a \times c \times e\) m. \(16x = 16 \times x\) b. \(8abc = 8 \times a \times b \times c\) d. \(7mn = 7 \times m \times n\) f. \(18m^2 = 18 \times m \times m\) h. \(9a^2b = 9 \times a \times a \times b\) j. \(8a^3 = 8 \times a \times a \times a\) 1. \(17a^2b^2 = 17 \times a \times a \times b \times b\) n. \(28x^2y^3 = 28 \times x \times x \times y \times y \times y\)

Solution

**a. \(28ab\)** - The expression shows multiplication of 28, \(a\), and \(b\). - In fully “expanded” (i.e. explicit multiplication) form we can write it as \[ 28ab = 28 \times a \times b. \] **c. \(7xy\)** - Here the factors are 7, \(x\), and \(y\). - Expanded form: \[ 7xy = 7 \times x \times y. \] **e. \(9abc\)** - This expression is the product of 9, \(a\), \(b\), and \(c\). - Written in expanded form: \[ 9abc = 9 \times a \times b \times c. \] **g. \(2xyz\)** - The factors are 2, \(x\), \(y\), and \(z\). - Therefore, \[ 2xyz = 2 \times x \times y \times z. \] **1. \(14mnp\)** - The expression multiplies 14, \(m\), \(n\), and \(p\). - In expanded multiplication form: \[ 14mnp = 14 \times m \times n \times p. \] **k. \(5ace\)** - The factors here are 5, \(a\), \(c\), and \(e\). - Thus, we have: \[ 5ace = 5 \times a \times c \times e. \] **m. \(16x\)** - This is simply 16 multiplied by \(x\). - Expanded form: \[ 16x = 16 \times x. \] Now, write the following expressions in expanded form: **b. \(8abc\)** - Factors: 8, \(a\), \(b\), \(c\). - Expanded: \[ 8abc = 8 \times a \times b \times c. \] **d. \(7mn\)** - Factors: 7, \(m\), \(n\). - Expanded: \[ 7mn = 7 \times m \times n. \] **f. \(18m^2\)** - Here \(m^2\) means \(m \times m\). With the coefficient 18, we write: \[ 18m^2 = 18 \times m \times m. \] **h. \(9a^2b\)** - \(a^2\) represents \(a \times a\). Therefore, \[ 9a^2b = 9 \times a \times a \times b. \] **j. \(8a^3\)** - \(a^3\) means \(a \times a \times a\). Thus, \[ 8a^3 = 8 \times a \times a \times a. \] **1. \(17a^2b^2\)** - Here \(a^2 = a \times a\) and \(b^2 = b \times b\). Hence, \[ 17a^2b^2 = 17 \times a \times a \times b \times b. \] **n. \(28x^2y^3\)** - \(x^2\) means \(x \times x\) and \(y^3\) means \(y \times y \times y\). So, \[ 28x^2y^3 = 28 \times x \times x \times y \times y \times y. \] Each expression is presented as the product of its numerical coefficient and its variables in expanded form.

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Bonus Knowledge

When you write expressions in expanded form, you're essentially breaking them down into a sum of terms. For example, the expression \( 7 m n \) in expanded form would simply remain as it is since it’s already a multiplication of two variables and doesn’t condense further. However, when you deal with something like \( 9 a^{2} b \), you can think of it as \( 9 \times a \times a \times b \), showcasing the individual components! Now, let’s connect this concept to your expressions. For \( 28 a b \), the expanded form is \( 28 \times a \times b \); for \( 8 a b c \), it transforms to \( 8 \times a \times b \times c \), embracing the beauty of variables playing together in your math expressions. Remember, every coefficient just reflects how many times you multiply those variables together!

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