A. In a graphing paper or bond paper, make your own algebraic tiles for addition and subtraction of algebraic expressions. Below the algebraic tiles, write the algebraic expression then solve. Example for Addition: (4x² - 6x + 6) + (-3x² + 4x + 4) = x² - 2x + 10 Example for Subtraction: (-6x² + 5x - 8) - (-3x² + 8x - 6) = -3x² - 3x - 2 B. Simplify the following and show your solutions. 1.) Add (12x - 8) and (-20x + 3). 2.) Subtract (9a²bc²) from (4a²bc²). 3.) Subtract (4m² - 2m + 10) by (m² + 6m - 4).

Let's simplify the algebraic expressions and solve the problems step-by-step.
B. Simplify the following and show your solutions.

Add

( 12 x − 8 )
and
( − 20 x + 3 )
.
To add these algebraic expressions, combine like terms:

Start with the x terms: 12 x + ( − 20 x ) = 12 x − 20 x = − 8 x .

Now, add the constant terms: − 8 + 3 = − 5.


So the result of addition is: 12 x − 8 + ( − 20 x + 3 ) = − 8 x − 5.

Subtract

( 9 a 2 b c 2 )
from
( 4 a 2 b c 2 )
.
Here you need to subtract the first expression from the second:

4 a 2 b c 2 − 9 a 2 b c 2 = ( 4 − 9 ) a 2 b c 2 = − 5 a 2 b c 2 .

So the result of subtraction is: 4 a 2 b c 2 − 9 a 2 b c 2 = − 5 a 2 b c 2 .

Subtract

( 4 m 2 − 2 m + 10 )
by
( m 2 + 6 m − 4 )
.
Subtract the second expression from the first:

Start with m 2 terms: 4 m 2 − m 2 = 3 m 2 .

Now, subtract the m terms: − 2 m − 6 m = − 8 m .

Finally, subtract the constant terms: 10 − ( − 4 ) = 10 + 4 = 14.


So the result of subtraction is: 4 m 2 − 2 m + 10 − ( m 2 + 6 m − 4 ) = 3 m 2 − 8 m + 14.
These steps help you to add or subtract algebraic expressions by combining like terms. It's a fundamental skill in algebra to simplify expressions or solve equations.

Answered by danjohnbrain | 2025-07-22