Expend the following 2(×+1)

Short answer

\[ 2(x+1)=2x+2 \]

(The "×" in your task is treated as the variable \(x\).)

Key steps

The rule is the distributive law: the number outside the bracket multiplies each term inside it.

\[ a(b+c)=ab+ac \]

So here \(a=2\), \(b=x\), \(c=1\):

1. \(2 \cdot x = 2x\)
2. \(2 \cdot 1 = 2\)
3. Add the results: \(\;2x+2\)

Brackets are no longer needed, because the terms \(2x\) and \(2\) are not like terms and cannot be combined.

Check

Pick any value, say \(x=3\):

• Original: \(2(3+1)=2\cdot 4=8\)
• Expanded: \(2\cdot 3+2=6+2=8\) ✓

Both give 8, so the expansion is correct.

Watch out: a common mistake is multiplying only the first term and writing \(2x+1\) — the 2 must reach both terms inside the bracket.