Combine Like Terms

Lesson Objective:

Students will be able to simplify expressions by combining like terms.

Student-Facing Learning Target:

I can combine like terms to simplify an expression.

Vocabulary:

1.) [b]Like Terms:[/b] terms that have the same variable raised to the same exponent[br]2.) [b]Coefficient:[/b] an integer that is written along with a variable [br]3.) [b]Invisible Coefficient: [/b]when there is no number in front of the variable the coefficient is 1

Do Now:

Alexis is trying to save to buy a TV, and puts money in her piggy bank to help her save. She puts $10 in her piggy bank 3 times a week.[br][br]Write as many different expressions as you can that represents the total money Alexis saved this week.

Part One: Combining Like Terms

When we have an expression or an equation with multiple terms, sometimes we can combine them to simplify our expression or equation. For example: [math]2x^2-3x+4x-12+15+10x^2[/math][br][br]When we see this expression we can see there are multiple terms but some have the same as others.[br]We can look to combine terms that have the same variable and the same exponents.[br][br]Looking at the expression above, we can identify multiple numbers that can be combined.[br][br][math]2x^2+10x^2[/math] Both have a variable of x and an exponent of 2 so we can combine them by adding the bases (the numbers) together to get [math]12x^2[/math].[br][br][math]-3x+4x[/math] Both have a variable of x and an exponent of 1 so we can combine them by using our integer rules to get [math]x[/math].[br][br][math]-12+5[/math] Both don't have any variables attached to them so we can combine them by using our integer rules to get [math]-7[/math].[br][br]Now we can put our answers together to get a simplified expression of: [math]12x^2+x-7[/math]