How do you combine like terms in (6n ^ { 3} - 7+ 6n ^ { 2} ) + ( 4- 7n ^ { 2} - 6n ^ { 4}) + (8n^4 - 8n )(6n3−7+6n2)+(4−7n2−6n4)+(8n4−8n)?

3 Answers
Nallasivam V
Aug 1, 2018

2n^4+6n^3-n^2-8n-32n4+6n3−n2−8n−3

Explanation:

Given -

(6n^3-7+6n^2)+(4-7n^2-6n^4)+(8n^4-8n)(6n3−7+6n2)+(4−7n2−6n4)+(8n4−8n)

6n^3-7+6n^2+4-7n^2-6n^4+8n^4-8n6n3−7+6n2+4−7n2−6n4+8n4−8n

-6n^4+8n^4+6n^3+6n^2-7n^2-8n-7+4−6n4+8n4+6n3+6n2−7n2−8n−7+4

2n^4+6n^3-n^2-8n-32n4+6n3−n2−8n−3

PJ
Aug 1, 2018

2n^4 + 6n ^ { 3} - n ^ { 2} - 8n - 32n4+6n3−n2−8n−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
+ (x + 1) = +1(x + 1) = (1*x) + (1*1) = x+1+(x+1)=+1(x+1)=(1⋅x)+(1⋅1)=x+1

- (x + 1) = -1(x + 1) = (-1*x ) + (-1*1) = -x-1−(x+1)=−1(x+1)=(−1⋅x)+(−1⋅1)=−x−1
(multiplying by a negative changes the sign)

a(x + 1) = a*x + a*1 = ax + aa(x+1)=a⋅x+a⋅1=ax+a
-a(x + 1) = -a*x - a*1 = -ax - a−a(x+1)=−a⋅x−a⋅1=−ax−a
-a(x - 1) = -a*x + a*1 = -ax + a−a(x−1)=−a⋅x+a⋅1=−ax+a

In this question:

(6n ^ { 3} - 7+ 6n ^ { 2} ) + ( 4- 7n ^ { 2} - 6n ^ { 4}) + (8n^4 - 8n )(6n3−7+6n2)+(4−7n2−6n4)+(8n4−8n)
All these brackets have + in front of them, so we can remove the brackets and all terms are unchanged.

6n ^ { 3} - 7+ 6n ^ { 2} + 4- 7n ^ { 2} - 6n ^ { 4} + 8n^4 - 8n 6n3−7+6n2+4−7n2−6n4+8n4−8n

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

+ 8n^4 - 6n ^ { 4} + 6n ^ { 3} - 7n ^ { 2} + 6n ^ { 2} - 8n - 7 + 4+8n4−6n4+6n3−7n2+6n2−8n−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:

8n^4 - 6n ^ { 4} + 6n ^ { 3} - 7n ^ { 2} + 6n ^ { 2} - 8n - 7 + 48n4−6n4+6n3−7n2+6n2−8n−7+4

2n^4 + 6n ^ { 3} - n ^ { 2} - 8n - 32n4+6n3−n2−8n−3

Jacobi J.
Aug 2, 2018

2n^4+6n^3-n^2-8n-32n4+6n3−n2−8n−3

Explanation:

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

Paying close attention to the sign, we get

2n^4+6n^3-n^2-8n-32n4+6n3−n2−8n−3

Hope this helps!

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