Powers · Add & subtract powers · 2.3

Subtract like powers.

Subtracting like terms works the same way: subtract the coefficients and keep the exponent. 7x³ − 2x³ = 5x³.

01 / THE IDEA

See it work.

Watch the method

Subtract like powers

7x³ − 2x³ = 5x³.

1 / 2
7x3−2x37x^{3} - 2x^{3}
1

Like terms?

Same base and same exponent — these are like terms.

7x3−2x37x^{3} - 2x^{3}
2

Combine the coefficients

Add (or subtract) the coefficients; the exponent does NOT change.

=5x3= 5 x^{3}
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type with ^ for powers — e.g. x^5.

streak 0
best 0
… =
— / WHY IT WORKS

The idea underneath.

Coefficients subtract

Like terms subtract by their coefficients; the power is unchanged.

Why it works

7 cubes − 2 cubes = 5 cubes.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Simplify 9x^4 - 5x^4

1

Like terms?

Same base and same exponent — these are like terms. 9x^4 - 5x^4

2

Combine the coefficients

Add (or subtract) the coefficients; the exponent does NOT change. = 4 x^4

EX 2medium

Simplify 4x^2 - 3x^2

1

Like terms?

Same base and same exponent — these are like terms. 4x^2 - 3x^2

2

Combine the coefficients

Add (or subtract) the coefficients; the exponent does NOT change. = x^2

EX 3hard

Simplify 9y^2 - 5y^2

1

Like terms?

Same base and same exponent — these are like terms. 9y^2 - 5y^2

2

Combine the coefficients

Add (or subtract) the coefficients; the exponent does NOT change. = 4 y^2

04 / COMMON TRAPS

Where students slip.

Trap

Subtracting the exponents.

Fix

The exponent stays; only coefficients change.

Trap

Dropping the variable part.

Fix

Keep x³ on the answer.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Simplify 4z^2 - 2z^2

Need a hint?
  • Subtract the coefficients.
  • Keep the exponent.
C2

Simplify 7y^2 - 4y^2

Need a hint?
  • Subtract the coefficients.
  • Keep the exponent.
C3

Simplify 7z^4 - 1z^4

Need a hint?
  • Subtract the coefficients.
  • Keep the exponent.
C4

Simplify 8x^4 - 7x^4

Need a hint?
  • Subtract the coefficients.
  • Keep the exponent.
Apply

Apply (4)

A1

Simplify 9y^3 - 7y^3

Need a hint?
  • Subtract the coefficients.
  • Keep the exponent.
A2

Simplify 5z^4 - 2z^4

Need a hint?
  • Subtract the coefficients.
  • Keep the exponent.
A3

Simplify 7x^2 - 4x^2

Need a hint?
  • Subtract the coefficients.
  • Keep the exponent.
A4

Simplify 8z^3 - 1z^3

Need a hint?
  • Subtract the coefficients.
  • Keep the exponent.
Extension

Extension (4)

E1

Simplify 9z^2 - 3z^2

Need a hint?
  • Subtract the coefficients.
  • Keep the exponent.
E2

Simplify 6x^4 - 1x^4

Need a hint?
  • Subtract the coefficients.
  • Keep the exponent.
E3

Simplify 7y^4 - 4y^4

Need a hint?
  • Subtract the coefficients.
  • Keep the exponent.
E4

Simplify 7y^2 - 1y^2

Need a hint?
  • Subtract the coefficients.
  • Keep the exponent.