Barrett Schwartz
02/09/2023 · Elementary School
The expression \( 2 x-(2 x+3)^{2}+4(x-1)+x^{3} \) can be simplified into the form \( A x^{3}+B x^{2}+C x+D \). Find the missing constants \( A, B, C \), and \( D \) below. \( A=\square \) \( B=\square \) \( C=\square \) \( D=\square \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
Expand the expression \( 2x-(2x+3)^2+4(x-1)+x^3 \)
Simplify the expression by following steps:
- step0: Calculate:
\(2x-\left(2x+3\right)^{2}+4\left(x-1\right)+x^{3}\)
- step1: Expand the expression:
\(2x-\left(4x^{2}+12x+9\right)+4\left(x-1\right)+x^{3}\)
- step2: Remove the parentheses:
\(2x-4x^{2}-12x-9+4\left(x-1\right)+x^{3}\)
- step3: Expand the expression:
\(2x-4x^{2}-12x-9+4x-4+x^{3}\)
- step4: Calculate:
\(-6x-4x^{2}-13+x^{3}\)
The expanded form of the expression \(2x-(2x+3)^2+4(x-1)+x^3\) is \(-6x-4x^{2}-13+x^{3}\).
Comparing this with the form \(Ax^{3}+Bx^{2}+Cx+D\), we can see that:
- \(A = 1\)
- \(B = -4\)
- \(C = -6\)
- \(D = -13\)
Therefore, the missing constants are:
- \(A = 1\)
- \(B = -4\)
- \(C = -6\)
- \(D = -13\)
Quick Answer
- \(A = 1\)
- \(B = -4\)
- \(C = -6\)
- \(D = -13\)
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