Powers · Add & subtract powers · 2.2

Add like powers.

To add like terms, add the coefficients and KEEP the exponent. 3x² + 5x² = 8x². You do NOT add the exponents — the power stays the same.

01 / THE IDEA

See it work.

Watch the method

Add like powers

3x² + 5x² = 8x² (3 + 5 = 8, exponent stays 2).

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3x2+5x23x^{2} + 5x^{2}
1

Like terms?

Same base and same exponent — these are like terms.

3x2+5x23x^{2} + 5x^{2}
2

Combine the coefficients

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

=8x2= 8 x^{2}
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type with ^ for powers — e.g. x^5.

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— / WHY IT WORKS

The idea underneath.

Coefficients add

x² + x² is two of the same thing, so count them: 3x² + 5x² = 8x². The exponent stays 2.

Why it works

3 apples + 5 apples = 8 apples — still apples.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Simplify 6y^3 + 2y^3

1

Like terms?

Same base and same exponent — these are like terms. 6y^3 + 2y^3

2

Combine the coefficients

Add (or subtract) the coefficients; the exponent does NOT change. = 8 y^3

EX 2medium

Simplify 5y^4 + 2y^4

1

Like terms?

Same base and same exponent — these are like terms. 5y^4 + 2y^4

2

Combine the coefficients

Add (or subtract) the coefficients; the exponent does NOT change. = 7 y^4

EX 3hard

Simplify 5x^4 + 7x^4

1

Like terms?

Same base and same exponent — these are like terms. 5x^4 + 7x^4

2

Combine the coefficients

Add (or subtract) the coefficients; the exponent does NOT change. = 12 x^4

04 / COMMON TRAPS

Where students slip.

Trap

Adding the exponents (getting x⁴).

Fix

Adding terms keeps the exponent; only multiplying adds exponents.

Trap

Forgetting the variable.

Fix

Keep x²; only the coefficient changes.

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 5z^2 + 2z^2

Need a hint?
  • Add only the coefficients.
  • Keep the exponent the same.
C2

Simplify 7y^2 + 5y^2

Need a hint?
  • Add only the coefficients.
  • Keep the exponent the same.
C3

Simplify 2y^3 + 8y^3

Need a hint?
  • Add only the coefficients.
  • Keep the exponent the same.
C4

Simplify 7x^4 + 2x^4

Need a hint?
  • Add only the coefficients.
  • Keep the exponent the same.
Apply

Apply (4)

A1

Simplify 8x^2 + 7x^2

Need a hint?
  • Add only the coefficients.
  • Keep the exponent the same.
A2

Simplify 6z^2 + 4z^2

Need a hint?
  • Add only the coefficients.
  • Keep the exponent the same.
A3

Simplify 8z^3 + 5z^3

Need a hint?
  • Add only the coefficients.
  • Keep the exponent the same.
A4

Simplify 2x^3 + 8x^3

Need a hint?
  • Add only the coefficients.
  • Keep the exponent the same.
Extension

Extension (4)

E1

Simplify 4y^4 + 5y^4

Need a hint?
  • Add only the coefficients.
  • Keep the exponent the same.
E2

Simplify 7z^3 + 5z^3

Need a hint?
  • Add only the coefficients.
  • Keep the exponent the same.
E3

Simplify 2y^3 + 5y^3

Need a hint?
  • Add only the coefficients.
  • Keep the exponent the same.
E4

Simplify 6y^3 + 2y^3

Need a hint?
  • Add only the coefficients.
  • Keep the exponent the same.