Algebra Basics · grades 7–10
Simplifying expressions.
One tiny step at a time, from plain numbers to powers. Tap-and-combine algebra tiles, an animated step simplifier, and a practice pad that checks your work is fully simplified — not just equal.
Just Numbers
The grammar of an expression: terms and order of operations.
- A1
What is an expression?
Numbers joined by operations — it has one value.
- A2
Terms carry their sign
The + and − split an expression into terms.
- A3
A term can be a product
× and ÷ bind tighter, so 4 × 2 is one term.
- A4
Brackets first
Brackets override the usual order.
- A5
Rearrange & regroup
Reorder a sum to add the easy pairs first.
- A6
Negatives
Subtracting more than you have gives a negative.
One Variable
Coefficients, like terms, and distributing.
- B1
A variable is a number
A letter stands for a number we do not know yet.
- B2
The coefficient
3x means 3 · x; a lone x means 1x.
- B3
Like vs unlike terms
Only terms with the same variable part can combine.
- B4
Combine like terms
Add the coefficients: 2x + 5x = 7x.
- B5
Keep constants separate
Collect the xs; leave the number on its own.
- B6
Subtract like terms
8x − 3x = 5x; and 6x − x = 5x.
- B7
Negative coefficients
When you subtract more, the coefficient goes negative.
- B8
Multiply a number by a term
4 · 3x = 12x — multiply the coefficients.
- B9
Distribute over a sum
3(x + 2) = 3x + 6 — multiply each term.
- B10
Distribute with a minus
−(x + 5) = −x − 5; −2(x − 3) = −2x + 6.
- B11
Distribute then collect
2(x + 4) + 3x = 5x + 8.
- B12
One-variable mastery
Mixed brackets, signs, and collecting.
Two Variables
Keep each letter in its own pile — and the product xy.
- C1
Different letters
3x + 2y cannot be combined.
- C2
Collect each letter
Gather the xs and the ys separately.
- C3
Subtract with two variables
6x + 4y − 2x − 5y = 4x − y.
- C4
Distribute over two
2(x + y) = 2x + 2y.
- C5
Distribute then collect (2)
2(x + y) + 4x = 6x + 2y.
- C6
The product xy
x · y = xy; 3x · 2y = 6xy; a new term type.
- C7
Two-variable mastery
Mixed two-variable simplifying.
Three Variables
Same rules, three piles.
Powers
x² is not 2x — combine, multiply, and distribute powers.
- E1
What is a power?
x · x = x²; the exponent counts the factors.
- E2
x² and x are not alike
Different powers are different terms.
- E3
Combine like powers
2x² + 5x² = 7x².
- E4
Collect by power
x² + 2x + 3x² + x = 4x² + 3x.
- E5
Multiply, add exponents
x² · x³ = x⁵ — add the exponents.
- E6
Coefficient × power
3x · 2x = 6x² — multiply numbers, add exponents.
- E7
Distribute a variable
x(x + 3) = x² + 3x.
- E8
Powers mastery
Mixed powers: collect, multiply, distribute.
Capstone
Put it all together: the full simplifying method.