# How do you combine like terms in (6n ^ { 3} - 7+ 6n ^ { 2} ) + ( 4- 7n ^ { 2} - 6n ^ { 4}) + (8n^4 - 8n )?

Aug 1, 2018

#### Answer:

$2 {n}^{4} + 6 {n}^{3} - {n}^{2} - 8 n - 3$

#### Explanation:

Given -

$\left(6 {n}^{3} - 7 + 6 {n}^{2}\right) + \left(4 - 7 {n}^{2} - 6 {n}^{4}\right) + \left(8 {n}^{4} - 8 n\right)$

$6 {n}^{3} - 7 + 6 {n}^{2} + 4 - 7 {n}^{2} - 6 {n}^{4} + 8 {n}^{4} - 8 n$

$- 6 {n}^{4} + 8 {n}^{4} + 6 {n}^{3} + 6 {n}^{2} - 7 {n}^{2} - 8 n - 7 + 4$

$2 {n}^{4} + 6 {n}^{3} - {n}^{2} - 8 n - 3$

Aug 1, 2018

#### Answer:

$2 {n}^{4} + 6 {n}^{3} - {n}^{2} - 8 n - 3$

#### Explanation:

Use BEDMAS or PEDMAS (use the one you have been taught, they do the same thing) to simplify :

First: B (= brackets), or P (= parentheses).

When removing brackets, multiply each term by the quantity outside the brackets.

If the quantity outside the brackets is 1, the 1 is not needed and normally not shown.

Five examples
$+ \left(x + 1\right) = + 1 \left(x + 1\right) = \left(1 \cdot x\right) + \left(1 \cdot 1\right) = x + 1$

$- \left(x + 1\right) = - 1 \left(x + 1\right) = \left(- 1 \cdot x\right) + \left(- 1 \cdot 1\right) = - x - 1$
(multiplying by a negative changes the sign)

$a \left(x + 1\right) = a \cdot x + a \cdot 1 = a x + a$
$- a \left(x + 1\right) = - a \cdot x - a \cdot 1 = - a x - a$
$- a \left(x - 1\right) = - a \cdot x + a \cdot 1 = - a x + a$

In this question:

$\left(6 {n}^{3} - 7 + 6 {n}^{2}\right) + \left(4 - 7 {n}^{2} - 6 {n}^{4}\right) + \left(8 {n}^{4} - 8 n\right)$
All these brackets have + in front of them, so we can remove the brackets and all terms are unchanged.

$6 {n}^{3} - 7 + 6 {n}^{2} + 4 - 7 {n}^{2} - 6 {n}^{4} + 8 {n}^{4} - 8 n$

Rearranging the expression so like terms are together (and in order):

$+ 8 {n}^{4} - 6 {n}^{4} + 6 {n}^{3} - 7 {n}^{2} + 6 {n}^{2} - 8 n - 7 + 4$

Second: E = exponents. Evaluate exponents where possible.
In this expression there are no exponents that can be evaluated or simplified.

Third: D = divide and M = multiply. There are no divisions or multiplications here.

Fourth: A = add and S = subtract. Only like terms can be added or subtracted. Different powers of an unknown are not like terms.

Adding/subtracting like terms simplifies the expression:

$8 {n}^{4} - 6 {n}^{4} + 6 {n}^{3} - 7 {n}^{2} + 6 {n}^{2} - 8 n - 7 + 4$

$2 {n}^{4} + 6 {n}^{3} - {n}^{2} - 8 n - 3$

Aug 2, 2018

#### Answer:

$2 {n}^{4} + 6 {n}^{3} - {n}^{2} - 8 n - 3$

#### Explanation:

The key realization is that we can combine terms with the same degree.

Paying close attention to the sign, we get

$2 {n}^{4} + 6 {n}^{3} - {n}^{2} - 8 n - 3$

Hope this helps!