Expand and factor expressions with negative rational numbers.
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In Lessons 3 and 4, students expand and factor expressions with rational numbers. In Lesson 4, students see negative numbers both inside and outside a parentheses group. They will need to recall rules of multiplying signed numbers, specifically a negative times a negative is a positive number.
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For each problem, fill in the blanks around the diagram, and then write equivalent expressions in the form:
___ ( _______) = ___________
What are the values of $$q$$ and $$r$$ in each set of equivalent expressions?
a. $$q(6x+4)=3x+r$$
b. $$q\left ( \frac{1}{2}x+\frac{1}{3} \right ) = 3x+r$$
c. $$q(3x+4)=r-8$$
Expand or factor each expression.
a. $${-\frac{1}{2}(-5x+4y-16)}$$
b. $${-2\left ( 4-\frac{1}{2}h \right )}$$
c. $${-\left ( \frac{2}{3}a-\frac{3}{4}b-1 \right )}$$
d. $${-16xy+8y}$$
e. $${\frac{1}{2}x-1}$$
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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
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The table below includes expressions that are written in expanded form and in factored form. Complete the table. Use a diagram if needed.
Factored Form | Expanded Form |
$$-5(a-b+1)$$ | |
$$18xy-6y$$ | |
$$-\frac{2}{5}(-20x+10y)$$ | |
$$-12d+9e-15$$ |
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