Warm Up Solutions

Multiply.
${(2 x - 3)}^{2}$

$(2 x - 3) (2 x - 3) 4 x^{2} - 6 x - 6 x + 9 4 x^{2} - 12 x + 9$

Multiply.
$(4 x - 3) (x - 3)$

$4 x^{2} - 12 x - 3 x + 9 4 x^{2} - 15 x + 9$

Note

Q: What are the similarities and differences between problem 1 and 2?
A: The leading coefficient and constant are the same values. The linear (middle) term is different between the problems.

Solve.
$7 x - \frac{1}{2} (2 x - 6) = 6 x + 3$

$\begin{array}{rcl} 7 x - x + 3 & = & 6 x + 3 \\ 6 x + 3 & = & 6 x + 3 \\ All real numbers, ℝ \end{array}$

Note

You could also write, 3 = 3, or 0 = 0. The result is the identity with the solution of all real numbers.

Note

You may be able to write the answer without showing all of the steps.