In 5x² − 3x + 7 the parts separated by plus and minus are terms. 5 and −3 are coefficients.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Like terms
Terms with the same variable to the same power can be combined. 5x and 3x can; 5x and 3x² cannot.
Distributing
3(2x + 5) means three lots of the whole bracket, giving 6x + 15.
Read the structure first
x² − 9 is a difference of two squares. Seeing that saves work later, and it is a property of how it is built.
Read the structure before you touch it
An expression has parts: terms separated by plus and minus, and factors multiplied within a term. In 5x² − 3x + 7 there are three terms, and the first has factors 5, x and x. Identifying the parts before rewriting is what stops you applying a rule where it does not fit.
Coefficients, variables and constants
In 5x², the 5 is the coefficient, x is the variable and the 2 is the exponent. The 7 in the expression is a constant — its value never changes. Naming these parts makes it possible to describe what you did to an expression rather than just showing it.
Rewriting never changes the value
Every legal manipulation — collecting like terms, distributing, factoring — produces an expression that evaluates identically for every input. If your rewriting gives a different value at some test number, it was not legal. Substituting a value is the cheapest possible check.
Why one form beats another
Factored form reveals roots; expanded form is easy to add; vertex form shows a parabola's turning point. There is no single "simplest" form — there is the form that answers your question. Choosing it deliberately is the skill Algebra 1 is really teaching.
Step 2: Try It Yourself
Tap and try it out.
203
5
10015
- 20 × 5100
- 3 × 515
- 23 × 5115
The four pieces cover the whole rectangle, so their areas add to 23 × 5.
Step 3: Watch an Example
One step at a time.
Watch Maya Simplify 4(2x − 3) + 5x
Maya simplifies an expression in two moves.
- Step 1
She distributes the 4 across both terms, giving 8x − 12.
Step 4: Your Turn
Practice makes it stick.
Combining
Problem 1 of 2
7x + 4x simplifies to how many x?
Distributing
Problem 2 of 2
6(x + 4) expands to 6x + what?
Read and Rewrite
1 of 4
5(2x + 3) expands to 10x + what?
2 of 4
9x − 2x simplifies to how many x?
3 of 4
In 4x² − 7x + 2, what is the coefficient of x?
4 of 4
Can 3x and 3x² be combined?
Step 5: Quick Check
Show what you know.
Question 1 of 2
3(4x − 2) expands to 12x − what?
Question 2 of 2
What makes two terms like terms?
What You Learned
- Terms are separated by plus and minus signs.
- Only like terms combine.
- Distributing multiplies everything inside the bracket.