Question

Subtract 3x – 7x3 + 5x2 from the sum of 2 + 8x2 – x3 and 2x3 – 3x2 + x - 2.​

Answer 1

Answer:

Simplify (6x3 – 2x2 + 8x) – (4x3 – 11x + 10)

Here's the subtraction, done horizontally:

(6x3 – 2x2 + 8x) – (4x3 – 11x + 10)

(6x3 – 2x2 + 8x) – 1(4x3 – 11x + 10)

(6x3 – 2x2 + 8x) – 1(4x3) – 1(–11x) – 1(10)

6x3 – 2x2 + 8x – 4x3 + 11x – 10

6x3 – 4x3 – 2x2 + 8x + 11x – 10

2x3 – 2x2 + 19x – 10

Going vertically, I'll write out the polynomials, leaving gaps as necessary:

\small{ \begin{array}{rrrr}6x^3&-2x^2&+8x& \\4x^3& &-11x&+10\\ \hline \end{array} }

6x

3

4x

3

−2x

2

+8x

−11x

+10

Then I'll flip all of the signs in the second line, and then add down:

\small{ \begin{array}{rrrr}6x^3&-2x^2&+8x& \\\textcolor{red}{\textbf{--}}4x^3& &\textcolor{red}{\textbf{+}}11x&\textcolor{red}{\textbf{--}}10\\ \hline 2x^3&-2x^2&+19x&-10\end{array} }

6x

3

–4x

3

2x

3

−2x

2

−2x

2

+8x

+11x

+19x

–10

−10

Either way, I get the same answer:

2x3 – 2x2 + 19x – 10

Answer 2

Answer:

Simplify (6x3 – 2x2 + 8x) – (4x3 – 11x + 10)

Here's the subtraction, done horizontally:

(6x3 – 2x2 + 8x) – (4x3 – 11x + 10)

(6x3 – 2x2 + 8x) – 1(4x3 – 11x + 10)

(6x3 – 2x2 + 8x) – 1(4x3) – 1(–11x) – 1(10)

6x3 – 2x2 + 8x – 4x3 + 11x – 10

6x3 – 4x3 – 2x2 + 8x + 11x – 10

2x3 – 2x2 + 19x – 10

Going vertically, I'll write out the polynomials, leaving gaps as necessary:

\small{ \begin{array}{rrrr}6x^3&-2x^2&+8x& \\4x^3& &-11x&+10\\ \hline \end{array} }

6x

3

4x

3

−2x

2

+8x

−11x

+10

Then I'll flip all of the signs in the second line, and then add down:

\small{ \begin{array}{rrrr}6x^3&-2x^2&+8x& \\\textcolor{red}{\textbf{--}}4x^3& &\textcolor{red}{\textbf{+}}11x&\textcolor{red}{\textbf{--}}10\\ \hline 2x^3&-2x^2&+19x&-10\end{array} }

6x

3

–4x

3

2x

3

−2x

2

−2x

2

+8x

+11x

+19x

–10

−10

Either way, I get the same answer:

2x3 – 2x2 + 19x – 10