A minus sign before a parenthesis

Do you know how to deal with negative numbers, and how to multiply them? Have you got a grip on parentheses? Good. Then let’s multiply with negative numbers inside parentheses. Here’s a parenthesis.

And here’s a negative number, in front of the parenthesis. We don’t even have to spell out the multiplication sign. If there’s no operation stated, then it’s multiplication. When we multiply with a parenthesis we multiply with each of the terms, one by one. Tag along.

Minus three times x equals minus three x. Minus three times two is minus six. Done. Now, let’s make it a bit more challenging, and choose an expression with a minus sign inside the parentheses too. Minus four times y minus six.

We do as always, multiply what’s in front of the parenthesis with each of the terms inside it: Minus four times y is minus four y. Minus four times minus six is...do you remember? Multiplying two negative numbers with each other is like removing debt. It’s something positive. Minus times minus is plus.

So, minus four times minus six is positive 24. Are you still following? If not, then go back and review how to multiply with negative numbers. Here’s one that might look a bit odd. Minus, parenthesis, z plus three.

What's this? Isn’t there supposed to be a number in front of the parentheses? Well. There is a number in front of the parentheses, but you can’t see it. A single minus sign in front of a parenthesis you can read as minus one.

Like this: That’s easier right? Minus one times z is minus z. Minus one times three is minus three. Look at the equation: compare what’s on the left hand side to what’s on the right. There was barely any calculation involved.

Multiplying with minus one, is the same thing as changing sign. Let’s test this rule in another calculation. Minus parenthesis x minus nine. Multiplying with minus one is the same thing as changing sign, so let’s change signs. x with opposite sign is minus x.

Minus nine with opposite sign is plus nine. Done. It doesn’t matter how many terms there are in the parentheses. Look here! A minus sign in front of a really long parenthesis: Minus, parenthesis, x minus y plus z minus 3.

Let’s change signs. x with opposite sign is minus x. Minus y with opposite sign is plus y. Plus z with opposite sign is minus z. Minus three with opposite sign is plus three.

And there’s the answer. When you see a lone minus sign in front of a parenthesis, you can remove it, if you change the signs of each of the terms inside the parentheses.