Testinar Grade 7 math

Expanding Expressions with the Distributive Property

Students will build Grade 7 mastery of expanding expressions with the distributive property using models, equations, and test-style reasoning.

CH04-03 Expressions

Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

Expand: \(4(2x-3)\)
1. \(6x-12\)
2. \(8x-12\)
3. \(8x-3\)
4. \(6x-7\)
Expand: \(3(x+5)\)
1. \(3x+5\)
2. \(3x+8\)
3. \(3x+15\)
4. \(x+15\)
Expand: \(-2(x+4)\)
1. \(-2x-8\)
2. \(-2x+8\)
3. \(2x-8\)
4. \(-2x+4\)
Expand: \(5(3y-2)\)
1. \(15y-2\)
2. \(8y-7\)
3. \(15y-10\)
4. \(3y-10\)
Expand: \(-3(2a-5)\)
1. \(-6a-15\)
2. \(-6a+15\)
3. \(6a-15\)
4. \(-6a-5\)
Expand: \(\frac{1}{2}(4x+6)\)
1. \(2x+3\)
2. \(4x+6\)
3. \(2x+6\)
4. \(x+3\)
Expand: \(6(m-1)\)
1. \(6m-6\)
2. \(6m-1\)
3. \(m-6\)
4. \(6m+6\)
Expand: \(7(2p+3)\)
1. \(14p+3\)
2. \(14p+10\)
3. \(14p+21\)
4. \(9p+10\)

Teacher and parent reference

Answer key and explanations

B. \(8x-12\)
Distribute \(4\) to both terms: \(4(2x)-4(3)=8x-12\). (Positive times negative gives negative.)
C. \(3x+15\)
Distribute \(3\) to both terms: \(3(x)+3(5)=3x+15\).
A. \(-2x-8\)
Distribute \(-2\): \(-2(x)-2(4)=-2x-8\). Negative times positive is negative.
C. \(15y-10\)
Distribute \(5\): \(5(3y)-5(2)=15y-10\).
B. \(-6a+15\)
Distribute \(-3\) to both terms: \(-3(2a)=-6a\) and \(-3(-5)=+15\) (negative times negative is positive). Result: \(-6a+15\).
A. \(2x+3\)
Distribute \(\frac{1}{2}\): \(\frac{1}{2}(4x)+\frac{1}{2}(6)=2x+3\).
A. \(6m-6\)
Distribute \(6\): \(6(m)-6(1)=6m-6\).
C. \(14p+21\)
Distribute \(7\): \(7(2p)+7(3)=14p+21\).