Factor Special Products: example 7.43

Factor: $81 y^{2} - 72 y + 16$ .

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Factor: $64 y^{2} - 80 y + 25$ .

How did it go?


Are the first and last terms perfect squares?
Check the middle term.
Does is match ${(a - b)}^{2}$ ? Yes.
Write the square of a binomial.
Check by mulitplying.
${(9 y - 4)}^{2}$
${(9 y)}^{2} - 2 \cdot 9 y \cdot 4 + 4^{2}$
$81 y^{2} - 72 y + 16 ✓$


Are the first and last terms perfect squares?
Check the middle term.
Does is match ${(a - b)}^{2}$ ? Yes.
Write the square of a binomial.
Check by mulitplying.
${(9 y - 4)}^{2}$
${(9 y)}^{2} - 2 \cdot 9 y \cdot 4 + 4^{2}$
$81 y^{2} - 72 y + 16 ✓$