If 3a2 - (a - 7) + [-4(a2 - 9) + 4a] is equivalent to pa2 + qa + r, then what is the value of 5p + 3q - r?
Question
If 3a² - (a - 7) + [-4(a² - 9) + 4a] is equivalent to pa² + qa + r, then what is the value of 5p + 3q - r?
Solution
First, let's simplify the given expression 3a^2 - (a - 7) + [-4(a^2 - 9) + 4a].
This simplifies to 3a^2 - a + 7 - 4a^2 + 36 + 4a.
Combine like terms to get -a^2 + 3a + 43.
So, we have -a^2 + 3a + 43 = pa^2 + qa + r.
Comparing the coefficients, we get:
p = -1, q = 3, and r = 43.
The question asks for the value of 5p + 3q - r.
Substitute the values of p, q, and r into the equation to get:
5(-1) + 3(3) - 43 = -5 + 9 - 43 = -39.
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