Question

if c = 2x - 5x² - 9 and d = x² + 9x, find an expression that equals 3c + 2d in standard form. answer attempt 1 out of 2

Explanation:

Step1: Substitute C and D

Substitute \( C = 2x - 5x^2 - 9 \) and \( D = x^2 + 9x \) into \( 3C + 2D \).
\( 3(2x - 5x^2 - 9) + 2(x^2 + 9x) \)

Step2: Distribute the coefficients

Distribute 3 and 2 into the parentheses.
\( 6x - 15x^2 - 27 + 2x^2 + 18x \)

Step3: Combine like terms

Combine the \( x^2 \) terms, \( x \) terms, and constant terms.
For \( x^2 \): \( -15x^2 + 2x^2 = -13x^2 \)
For \( x \): \( 6x + 18x = 24x \)
Constant term: \( -27 \)
So the expression is \( -13x^2 + 24x - 27 \)

Answer:

\( -13x^2 + 24x - 27 \)