Squaring a bracket

First squared, last squared, and twice the two multiplied in the middle.

The question

Expand (x + 5)²

The trick

(a + b)² = a² + 2ab + b². Square the first, square the last, and put double their product in between.

Worked example

1First squared: x²
2Twice the product: 2 × x × 5 = 10x
3Last squared: 25
4Together: x² + 10x + 25

So: x² + 10x + 25

Remember it like this

First, twice, last. Say it as a little chant — the middle term is the one everybody forgets.

In the exam

The single most common mistake in all of algebra is writing (a+b)² = a² + b². It is wrong, and examiners test it deliberately. For (a − b)² only the middle term turns negative: (x − 4)² = x² − 8x + 16.

Why it works

(a+b)² is just (a+b)(a+b). Multiplying out gives a² + ab + ba + b², and the two identical middle terms combine into 2ab.

Explain this to my childGet the words to teach it, in your language

Try it yourself

0/3 correct

1
Expand (x + 3)²
Expand (x + 3)²
2
Expand (x − 4)²
Expand (x − 4)²
3
Expand (2x + 1)²
Expand (2x + 1)²