Andrea S. answered • 10/28/16

Master degree, lover of math and learning, homeschool Mom

The 2nd one is easier than the first so I'll start with that

(x + y)(x - y) = x2 - y2 is the formula. When you multiply the two parenthetical terms (x+y) and (x-y) together, you get

x2 + xy - xy - y2. Since the middle two terms cancel each other out, the result is x2 - y2 which is the same format as your equation.

So in your problem you simply need to figure out the square root of each of your terms. The square root of 16m2 is 4m (4m x 4m = 16m2). The square root of your 2nd term is 11. So going with the known formula above, you would end up with (4m + 11)(4m - 11) as your answer. Multiple those two together to confirm that your math was correct to see that the result is 16m2 + 44m - 44m - 121 = 16m2 - 121.

Now the first equation. You are looking for some form of (ax + by)(cx + dy), with a,b,c, and d being your coefficients (numbers). it takes some trial and error to find the answer. First, you need to figure out what possible coefficients you can have:

for your first term (the term containing the y

(x + y)(x - y) = x2 - y2 is the formula. When you multiply the two parenthetical terms (x+y) and (x-y) together, you get

x2 + xy - xy - y2. Since the middle two terms cancel each other out, the result is x2 - y2 which is the same format as your equation.

So in your problem you simply need to figure out the square root of each of your terms. The square root of 16m2 is 4m (4m x 4m = 16m2). The square root of your 2nd term is 11. So going with the known formula above, you would end up with (4m + 11)(4m - 11) as your answer. Multiple those two together to confirm that your math was correct to see that the result is 16m2 + 44m - 44m - 121 = 16m2 - 121.

Now the first equation. You are looking for some form of (ax + by)(cx + dy), with a,b,c, and d being your coefficients (numbers). it takes some trial and error to find the answer. First, you need to figure out what possible coefficients you can have:

for your first term (the term containing the y

^{2}you can factor the number as 1x27, 3x9, 9x3, or 27x1. For your final term, you can have 1x28, 2x14, 4x7, 7x4, 14x2, or 28x1.Explaining how to reason through the process of selecting your coefficients takes a bit more time than works in this venue. I can give you the answer here (3y - 4)(9y - 7), but it won't help you know how to do it yourself on future problems. Feel free to contact me for tutoring help if desired.