Answer
a) $18$
b) $18$
c) In both methods, we used the correct properties of real numbers and followed the order of operations, and since we evaluated the same or equivalent expressions, its value for $x = 3$ must be the same regardless of the method used.
Work Step by Step
a) To evaluate, we plug in $3$ to $x$:
$2(2x^{2}–x) –3(x^{2}–x) + x^{2}–x$
= $2(2(3)^{2}–3) –3(3^{2}–3) + 3^{2}–3$
= $2(2(9)–3) –3(9–3) + 9–3$
= $2(18–3) –3(6) + 6$
= $2(15) – 18 + 6$
= $30 – 18 + 6$
= $18$
b) Simplifying first, we get:
$2(2x^{2}–x) –3(x^{2}–x) + x^{2}–x$
= $4x^{2}–2x –3x^{2}+3x+ x^{2}–x$
= $2x^{2}$
Now we plug in $3$ to $x$:
$2(3)^{2} = 2(9) = 18$
