Subtracting Polynomials

To subtract a polynomial in parentheses, subtract each of its terms. In $4x^{2}+x-\left(x^{2}-3x\right)$, the minus sign applies to both $x^{2}$ and $-3x$. Subtracting $x^{2}$ gives $-x^{2}$. Subtracting $-3x$ is the same as adding $3x$. So the expression becomes $4x^{2}+x-x^{2}+3x$.

When you remove parentheses with a minus sign in front, change the sign of every term inside. So $-\left(x^{2}-3x\right)$ becomes $-x^{2}+3x$. Then collect the like terms. The squared terms give $4x^{2}-x^{2} = 3x^{2}$, and the $x$ terms give $x+3x = 4x$. The result is $3x^{2}+4x$.

Subtracting $-3x$ is the same as adding $3x$, because two minus signs make a plus. When you remove parentheses with a minus sign in front, change the sign of every term inside, not only the first one.