# How do you subtract like terms in (4x ^ { 2} + 3x - 1) - 2x ( x ^ { 2} + 4x \div 2)?

May 18, 2018

See below.

#### Explanation:

Assuming that the terms that you would like to subtract can be written like this:

$\left(4 {x}^{2} + 3 x - 1\right) - 2 x \left({x}^{2} + \frac{4 x}{2}\right)$.

Because of the order of operations,

which dictates the order that we can perform binary operations (those listed above, in order from top to bottom), we cannot subtract the two terms just yet because, you will observe above, we cannot subtract before multiplying. Therefore we must first distribute the $2 x$ term before proceeding.

By the distributive property we know that

$a \left(b + c\right) = a b + a c$,

therefore:

$- 2 x \left({x}^{2} + \frac{4 x}{2}\right) = - 2 x \cdot x - 2 x \cdot \frac{4 x}{2}$.

Continuing:

$- 2 x \cdot x - 2 x \cdot \frac{4 x}{2} = - 2 {x}^{2} - \frac{8 {x}^{2}}{2} = - 2 {x}^{2} - 4 {x}^{2}$.

Combining like terms:

$- 2 {x}^{2} - 4 {x}^{2} = - 6 {x}^{2}$.

We can now subtract the two terms:

$\left(4 {x}^{2} + 3 x - 1\right) - 2 x \left({x}^{2} + \frac{4 x}{2}\right) = \left(4 {x}^{2} + 3 x - 1\right) - \left(6 {x}^{2}\right)$,

and we obtain:

$- 2 {x}^{2} + 3 x - 1$.