1. The Distributive Property & Combining Like Terms

2. y + xy 2(x + 5) = 2(x) + 2(5) 2x + 10 a(b + c) = ab + ac
USING THE DISTRIBUTIVE PROPERTY
THE DISTRIBUTIVE PROPERTY
The product of a and (b + c):
2(x + 5) =
2(x) + 2(5) =
2x + 10
a(b + c) = ab + ac
(b + c)a = ba + ca
(x + 5)2 =
(x)2 + (5)2 =
2x + 10
y(1 + x) =
y(1) +y(x) =
y + xy
(1 + 5x)2 =
(1)2 + (5x)2 =
2 + 10x
BACK

3. = –7 + 3x (–3)(1 + x) = (–3)(1) + (–3)(x) = –3 – 3x –(y – 5)
USING THE DISTRIBUTIVE PROPERTY
Remember that a factor must multiply each term of an expression.
Distribute the –3.
(–3)(1 + x)
= (–3)(1) + (–3)(x)
Simplify.
= –3 – 3x
–(y – 5)
= (y)(–1) + (–5)(–1)
Distribute the –1.
= –y + 5
Simplify.
= (–1)(7) + (–1)(–3x)
–a = –1 • a
–(7 – 3x)
Simplify.
= –7 + 3x
Forgetting to distribute the negative sign when multiplying by a negative factor is a common error.
BACK

4. = 5x2 - 4 8x + 3x + y = 11x +y 4x2 + 2 + x2 - 6 = 4x2 +1 x2 + 2 - 6
SIMPLIFYING BY COMBINING LIKE TERMS
Like Terms are expressions that contain the same variable raised to the same power like 4mn and 7mn.
8x + 3x + y =
11x +y
The 8x and 3x are like terms and can be combined.
4x x2 - 6 =
4x2 +1 x
Group like terms.
= 5x2 - 4
Combine like terms.
BACK

5. Combine like terms with parenthesis…
BACK

6. Objectives Use the Distributive Property to solve equations.
Solve real-world problems by using multistep equations.

7. Key Skills Solve 3(x - 4) = 48 Solve 3(x - 4) = 48
Use the distributive property.
3 * x + 3 * -4 = 48
Multiply
Add both sides of the = sign.
3x - 12 = 48
Divide both sides of the = sign by 3.
3x = 60
x = 20

8. Key Skills TRY THIS Solve 5(x +2) = 35 Solve 5(x +2) = 35
Use the distributive property.
5 * x + 5 * 2 = 35
Multiply
Subtract 10 from both sides of the = sign.
5x + 10 = 35
Divide both sides of the = sign by 3.
5x = 25
x = 5

9. Key Skills Combine like terms that are on the same side of the = sign.
Solve 3y – 8 –y = 6
Solve 3y – 8 –y = 6
2y – 8 = 6
Add 8 to both sides of the = sign.
2y = 14
Divide both sides of the equal sign by 2
y = 7

10. Key Skills
TRY THIS
Combine like terms that are on the same side of the = sign.
Solve 6y +2 –3y = 8
Solve 6y +2 –3y = 8
3y +2 = 8
Subtract 2 from both sides of the = sign.
3y = 6
Divide both sides of the equal sign by 3
y = 2

11. Key Skills Solve 4x -8(x + 1) = 8 4x -8(x + 1) = 8 Distribute -8
Multiply
4x -8x -8 = 8
4x -8x -8 = 8
Combine like terms.
-4x -8 = 8
Add 8 to both sides of the = sign.
-4x = 16
Divide both sides of the equal sign by -4
x = -4

12. Key Skills Use the Distributive Property to solve multistep equations.
Solve 8x – 2(3x – 4) = 5x – 7.
Solve 8x – 2(3x – 4) = 5x – 7.
Distributive -2
8x + (–2)(3x) + (–2)(–4) = 5x – 7
Multiply.
Combine like terms that are on the same side of the = sign.
8x – 6x + 8 = 5x – 7
8x – 6x + 8 = 5x – 7
2x + 8 = 5x – 7

13. Subtract 2x from both sides of the = sign.
2x + 8 = 5x – 7
-2x x
8 = 3x -7
Add 7 to both sides of the = sign.
Divide both sides of the = sign by 3
15 = 3x
5 = x

14. Key Skills
TRY THIS
Use the Distributive Property to solve multistep equations.
Solve 4y – 7(y +6) = 5y – 2.
Solve 4y – 7(y +6) = 5y – 2.
Distributive -7
4y + (–7)(y) + (–7)(+6) = 5y – 2
Multiply.
Combine like terms that are on the same side of the = sign.
4y – 7y -42 = 5y – 2
4y – 7y -42 = 5y – 2
-3y -42 = 5y – 2

15. Add 3y to both sides of the = sign.
-3y -42 = 5y – 2
+3y y
-42 = 8y -2
Add 2 to both sides of the = sign.
Divide both sides of the = sign by 8
-40 = 8y
-5 = y