Which expression is equivalent to 2x(3x - 4) - x^2? A) 5x^2

Step by step

The question

Question: simplify 2x(3x − 4) − x².

Simplify means: write it shorter, with the same value.

2x(3x − 4) − x²

There are four choices.

First we solve it, the normal way.

Then we pick.

1 Open the brackets

The 2x in front of the bracket multiplies every part inside.

a(b + c) = ab + ac

So we write 2x times each part.

= 2x(3x) + 2x(−4) − x²

− × + = −

x times x is x²: x squared.

x × x = x²

Watch the signs.

2x times 3x is 6x².

2x times (−4) is −8x.

= 6x² − 8x − x²

2 Group like terms

Terms are the parts between the + and − signs.

Like terms are the same kind: same letters, same powers.

All the x² terms go together.

Each colour is one kind.

like terms = same letters,

same powers

We move like terms next to each other.

Each term takes its sign with it.

= 6x² − x² − 8x

x² alone means 1x².

6x² − x² is 5x².

It is like 6 apples take away 1 apple: that is 5 apples.

x² = 1x²

6x² − x² = 5x²

So the expression is 5x² − 8x.

= 5x² − 8x

3 Check

Let's check.

We pick a small number for each letter: x = 2.

Any number works, and a small one keeps the sums easy.

We put it into the question.

Question: 2 × 2 × (3 × 2 − 4) − 2²

= 4 × 2 − 4 = 8 − 4 = 4

Now into our answer.

Answer: 5 × 2² − 8 × 2 = 20 − 16 = 4

Both give 4.

Same value, so 5x² − 8x is right!

Both give 4

4 Pick the choice

Our answer is 5x² − 8x.

That is choice A.

A) 5x² − 8x

5 Why not the others

B is 5x² − 4.

Wrong: 2x × (−4) is −8x, not −4.

B) 5x² − 4 ✗ 2x × (−4) is −8x, not −4

C is 7x² − 8x.

Wrong: 6x² + x²: added instead of taking away.

C) 7x² − 8x ✗ 6x² + x²: added instead of taking away

D is 6x² − 9x.

Wrong: took away x, not x².

D) 6x² − 9x ✗ took away x, not x²

Let's look back.

First: open the brackets.

Then: group like terms.

Then: check.

Then: pick the choice.

Last: why not the others.

Answer