#binomial squares

[pwnthesat]

Could you work out #10 on section 3 of Practice test #5?

Sure! You’re told that a^2 + b^2 = z and that ab = y. You want 4z + 8y, so you should write that out:

4z + 8y= 4(a^2 + b^2) + 8ab= 4a^2 + 8ab + 4b^2

If you’re slick with your binomial squares, you’ll recognize that right away as (2a + 2b)^2, which is choice B. If not, then the fastest way is probably to backsolve: FOIL out the answer choices until you match 4a^2 + 8ab + 4b^2.

[pwnthesat]

Hey! can you please explain number 18 in your Right Triangles post?

[My Right Triangles post.]

The difference between the square of a hypotenuse and the square of one leg, according to the Pythagorean Theorem, is simply the square of the other leg. 

So the question's really telling you that the square of the other leg is:

Conveniently, we can factor that very quickly if we know our binomial squares:

Remember, that's supposed to be the SQUARE of the other leg. So the other leg is simply x - y.