Simplified form

The idea

Rewriting an expression as an equal expression with fewer terms gives its simplified form.

Four terms or two?

Walking round a rectangle gives l + b + l + b, which has 4 terms. A friend writes the perimeter as 2l + 2b, which has only 2 terms.

Can an expression with 4 terms be rewritten with only 2 terms and keep the same value?

• Yes
• No: fewer terms must change the value
• Only if l and b are equal

Join the terms

Tap two terms with the same letter-number to join them. Watch the number of terms drop while the value stays the same.

Fewer terms, same value

2l + 2b has 2 terms and l + b + l + b has 4, yet they have the same value for every *l* and *b*.

Rewriting an expression as an equal expression with fewer terms gives its simplified form: 2l + 2b is the simplified form of l + b + l + b.

• Expression | Terms | Value when l = 3, b = 4
• l + b + l + b | 4 | 14
• 2l + 2b | 2 | 14

Notes

Rewriting an expression as an equal expression with fewer terms gives its simplified form.

Check yourself

Which is the simplified form of a + a + a?

The simplified form of l + b + l + b is 2l + 2b. Find its value when *l* = 6 and *b* = 5.

Answer: 22

2 × 6 + 2 × 5 = 12 + 10 = 22, and 6 + 5 + 6 + 5 = 22.

Why can 2x + y be called the simplified form of x + y + x?

x + y + x + y + x has 5 terms. Its simplified form is 3x + 2y. By how many terms did it shrink?

Answer: 3

5 − 2 = 3 terms fewer.

• a + 3. That adds 3 to a once. We need a added three times.
• 3a — correct. Yes! The letter-number a is added three times: 3 × a.
• a3. Write the number first: 3a.
• It is shorter, even if the value changes.. A simplified form must have exactly the same value.
• It has more terms than the original.. A simplified form has fewer terms.
• It has the same value for every x and y, and it has fewer terms (2, not 3). — correct. Yes! Equal, with fewer terms.