Let's think about how to simplify the following expression:

6x-(3+2x)

In this example, we're subtracting the entire group of terms in parentheses from 6x. In such cases, we distribute the negative sign to each term in the parentheses first and then simplify by collecting like terms.

Removing the parentheses by distributing the negative sign, we get

\begin{align*} 6x-(3+2x) &= \\[5pt] 6x - 3 - 2x&. \end{align*}

Finally, we collect like terms:

\begin{align*} 6x - 3 - 2x &=\\[5pt] (6x-2x) - 3 &=\\[5pt] 4x-3& \end{align*}

Let's take a look at another example.

FLAG

Simplify the expression -3-(5+2u).

EXPLANATION

First, we remove the parentheses by distributing the negative sign. This gives

-3 - 5 - 2u.

Finally, we collect like terms:

\begin{align*} -3 - 5 - 2u &=\\[5pt] (-3-5) - 2u &=\\[5pt] -8 - 2u& \end{align*}

FLAG

$5-(x+1)=$

a
$-4+x$
b
$4-x$
c
$6+x$
d
$6-x$
e
$4+x$

$-6-(2x+4)=$

a
$-2+2x$
b
$-10-2x$
c
$-8-x$
d
$-2-2x$
e
$-10+2x$

Simplify the expression 11-(5a-7).

EXPLANATION

First, we remove the parentheses by distributing the negative sign. This gives

11-5a + 7.

Finally, we collect like terms:

\begin{align*} 11-5a + 7 &= \\[5pt] (11+7) - 5a &= \\[5pt] 18-5a& \end{align*}

FLAG

Simplify the expression $4-(2h-3).$

a
$7+2h$
b
$2+2h$
c
$1+2h$
d
$1-2h$
e
$7-2h$

Simplify the expression $-3h-(2h-9).$

a
$-h-9$
b
$h-9$
c
$-h+9$
d
$-5h+9$
e
$-5h-9$

Sometimes, to subtract a group of terms, we have to apply the distributive law.

For example, let's simplify the following expression:

7-4(y+2)

First, let's write some big brackets around the expression in parentheses, keeping the minus sign outside.

7 - \Big[4(y+2)\Big]

Next, we expand the expression inside the brackets using the distributive law. This gives

7 - \Big[4y+8\Big].

Now, we proceed as before. Removing the brackets by distributing the negative sign gives

7 - 4y - 8.

Finally, we collect like terms:

\begin{align*} 7 - 4y - 8 &=\\[5pt] (7-8) - 4y &=\\[5pt] -1-4y& \end{align*}

FLAG

Simplify the expression -9v-4(3+5v).

EXPLANATION

Notice that the expression we need to subtract from -9v must be expanded using the distributive law.

So first, let's write some big brackets around the expression in parentheses, keeping the minus sign outside.

-9v - \Big[4(3+5v)\Big]

Next, we expand the expression inside the brackets using the distributive law. This gives

-9v - \Big[12+20v\Big].

Now, we remove the brackets by distributing the negative sign. This gives

-9v - 12 - 20v.

Finally, we collect like terms:

\begin{align*} -9v - 12 - 20v &=\\[5pt] (-9v-20v) - 12 &=\\[5pt] -29v-12& \end{align*}

FLAG

$5-3(x+1)=$

a
$2-3x$
b
$6-x$
c
$6-3x$
d
$2-x$
e
$2+3x$

$-6 - 2(3t + 5)=$

a
$4 - 6t$
b
$-16 - 6t$
c
$-4 - 6t$
d
$-16 + 6t$
e
$16 + 6t$

Simplify the expression 10 - 2(3x - 4).

EXPLANATION

Notice that the expression we need to subtract from 10 must be expanded using the distributive law.

So first, let's write some big brackets around the expression in parentheses, keeping the minus sign outside.

10 - \Big[2(3x-4)\Big]

Next, we expand the expression inside the brackets using the distributive law. This gives

10 - \Big[6x-8\Big].

Now, we remove the brackets by distributing the negative sign. This gives

10 - 6x + 8.

Finally, we collect like terms:

\begin{align*} 10 - 6x + 8 &=\\[5pt] (10+8) - 6x &=\\[5pt] 18-6x& \end{align*}

FLAG

$4-6(2h-3)=$

a
$22 - 12h $
b
$-4h+6$
c
$12h-18$
d
$20h+18$
e
$4h-6$

$-1-5(2v-1)=$

a
$4-5v$
b
$2-10v$
c
$2-12v$
d
$-1-5v$
e
$4-10v$
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