Which expression is equivalent to (3x)^2? A) 3x^2 {squared only the… Step by Step

Step by step

The question

Question: simplify (3x)².

(3x)²

There are four choices.

First we solve it, the normal way.

Then we pick.

1 Write the power out

The power 2 outside the bracket means: the whole bracket, 2 times.

(3x)² = (3x)(3x)

So we write the bracket out, times itself.

= ((3x))((3x))

2 Numbers with numbers

In times, the order does not matter.

So numbers go with numbers, and each letter goes with the same letter.

order does not matter: ab = ba

We put them in groups.

= (3 × 3)(x x)

3 Count the letters

A power tells how many times the letter is multiplied.

x is 1 x.

Together that is 2 x's multiplied.

x x = (x)(x) = x²

So the rule: when we multiply the same letter, we add the powers.

1 plus 1 is 2.

1 + 1 = 2

x^a x^b = x^{a + b}

3 times 3 is 9.

So we get 9x².

= 9x²

4 Pick the choice

Our answer is 9x².

That is choice D.

D) 9x²

5 Why not the others

A is 3x².

Wrong: squared only the x: 3 × 3 is 9.

A) 3x² ✗ squared only the x: 3 × 3 is 9

B is 6x².

Wrong: 3 × 2: but 3² is 3 × 3 = 9.

B) 6x² ✗ 3 × 2: but 3² is 3 × 3 = 9

C is 9x.

Wrong: squared only the 3: x × x is x².

C) 9x ✗ squared only the 3: x × x is x²

Let's look back.

First: write the power out.

Then: numbers with numbers.

Then: count the letters.

Then: pick the choice.

Last: why not the others.

Answer