Question
Which expression is equivalent to (7x^2+13x-19)-(4x+7-16x^2)
Answers
GPT-4o mini
To simplify the expression \((7x^2 + 13x - 19) - (4x + 7 - 16x^2)\), we first distribute the negative sign through the second set of parentheses:
\[
(7x^2 + 13x - 19) - (4x + 7 - 16x^2) = 7x^2 + 13x - 19 - 4x - 7 + 16x^2
\]
Next, we combine like terms:
1. For \(x^2\) terms: \(7x^2 + 16x^2 = 23x^2\)
2. For \(x\) terms: \(13x - 4x = 9x\)
3. For constant terms: \(-19 - 7 = -26\)
Putting it all together, we get:
\[
23x^2 + 9x - 26
\]
Thus, the expression equivalent to \((7x^2 + 13x - 19) - (4x + 7 - 16x^2)\) is:
\[
\boxed{23x^2 + 9x - 26}
\]
\[
(7x^2 + 13x - 19) - (4x + 7 - 16x^2) = 7x^2 + 13x - 19 - 4x - 7 + 16x^2
\]
Next, we combine like terms:
1. For \(x^2\) terms: \(7x^2 + 16x^2 = 23x^2\)
2. For \(x\) terms: \(13x - 4x = 9x\)
3. For constant terms: \(-19 - 7 = -26\)
Putting it all together, we get:
\[
23x^2 + 9x - 26
\]
Thus, the expression equivalent to \((7x^2 + 13x - 19) - (4x + 7 - 16x^2)\) is:
\[
\boxed{23x^2 + 9x - 26}
\]