Question

Add and subtract polynomials

10(u+v)+8(u-1)-3(u+6)

@michele_laino

Answer 1

What do I have to do first?

Answer 2

Simplifying
-10(u + v) + 8(u + -1) + -3(u + 6) = 0
(u * -10 + v * -10) + 8(u + -1) + -3(u + 6) = 0
(-10u + -10v) + 8(u + -1) + -3(u + 6) = 0

Reorder the terms:
-10u + -10v + 8(-1 + u) + -3(u + 6) = 0
-10u + -10v + (-1 * 8 + u * 8) + -3(u + 6) = 0
-10u + -10v + (-8 + 8u) + -3(u + 6) = 0

Reorder the terms:
-10u + -10v + -8 + 8u + -3(6 + u) = 0
-10u + -10v + -8 + 8u + (6 * -3 + u * -3) = 0
-10u + -10v + -8 + 8u + (-18 + -3u) = 0

Reorder the terms:
-8 + -18 + -10u + 8u + -3u + -10v = 0

Combine like terms: -8 + -18 = -26
-26 + -10u + 8u + -3u + -10v = 0

Combine like terms: -10u + 8u = -2u
-26 + -2u + -3u + -10v = 0

Combine like terms: -2u + -3u = -5u
-26 + -5u + -10v = 0

Solving
-26 + -5u + -10v = 0

Solving for variable 'u'.

Move all terms containing u to the left, all other terms to the right.

Add '26' to each side of the equation.
-26 + -5u + 26 + -10v = 0 + 26

Reorder the terms:
-26 + 26 + -5u + -10v = 0 + 26

Combine like terms: -26 + 26 = 0
0 + -5u + -10v = 0 + 26
-5u + -10v = 0 + 26

Combine like terms: 0 + 26 = 26
-5u + -10v = 26

Add '10v' to each side of the equation.
-5u + -10v + 10v = 26 + 10v

Combine like terms: -10v + 10v = 0
-5u + 0 = 26 + 10v
-5u = 26 + 10v

Divide each side by '-5'.
u = -5.2 + -2v

Simplifying
u = -5.2 + -2v

Answer 3

So, for the first part I have to distributive property. Correct?

Answer 4

yes

Answer 5

here you have to apply the distributive propery of multiplication over addition, so we can write:
\[\Large \begin{gathered}
10\left( {u + v} \right) + 8\left( {u - 1} \right) - 3\left( {u + 6} \right) = \hfill \\
\hfill \\
= 10u + 10v + 8u - 8 - 3u - 18 = ... \hfill \\
\end{gathered} \]
please simplify

Answer 6

Hint:
next step is:
\[\Large \begin{gathered}
10\left( {u + v} \right) + 8\left( {u - 1} \right) - 3\left( {u + 6} \right) = \hfill \\
\hfill \\
= 10u + 10v + 8u - 8 - 3u - 18 = \hfill \\
\hfill \\
= \left( {10 + 8 - 3} \right)u + 10v - 8 - 18 = ... \hfill \\
\end{gathered} \]

Answer 7

I am so confused

Answer 8

why?

Answer 9

you have to combine like terms

Answer 10

Is that correct?