Lesson 11
The Distributive Property, Part 3
Let's practice writing equivalent expressions by using the distributive property.
Problem 1
For each expression, use the distributive property to write an equivalent expression.
 \(4(x+2)\)
 \((6+8)\boldcdot x\)
 \(4(2x+3)\)
 \(6(x+y+z)\)
Problem 2
Priya rewrites the expression \(8y  24\) as \(8(y3)\). Han rewrites \(8y24\) as \(2(4y12)\). Are Priya's and Han's expressions each equivalent to \(8y24\)? Explain your reasoning.
Problem 3
Select all the expressions that are equivalent to \(16x + 36\).
\(16(x+20)\)
\(x(16+36)\)
\(4(4x+9)\)
\(2(8x+18)\)
\(2(8x+36)\)
Problem 4
The area of a rectangle is \(30 + 12x\). List at least 3 possibilities for the length and width of the rectangle.
Problem 5
Select all the expressions that are equivalent to \(\frac{1}{2}z\).
\(z + z\)
\(z \div 2\)
\(z \boldcdot z\)
\(\frac{1}{4}z + \frac{1}{4} z\)
\(2z\)
Problem 6

What is the perimeter of a square with side length:
3 cm?
7 cm?
\(s\) cm?
 If the perimeter of a square is 360 cm, what is its side length?

What is the area of a square with side length:
3 cm?
7 cm?
\(s\) cm?
 If the area of a square is 121 cm^{2}, what is its side length?
Problem 7
Solve each equation.
\(10=4a\)
\(5b=17.5\)
\(1.036=10c\)
\(0.6d=1.8\)
\(15=0.1e\)