Tricky Algebra Problem Using FOIL Polynomials & Quadratics SAT & ACT Math Prep #shorts #maths #math

[adilraziqwakil]

We can also solve this using the formula:
a² - b² = (a + b)(a - b)
or to not confuse for this particular question:
x² - y² = (x + y)(x - y)
Here, x = (a + b) and y = (a - b)
x² - y² = (x + y)(x - y)
⇒ (a + b)² - (a - b)² = (a + b + a - b)(a + b - (a - b))
⇒ (a + b)² - (a - b)² = (2a)(a + b - a + b)
⇒ (a + b)² - (a - b)² = (2a)(2b)
⇒ (a + b)² - (a - b)² = 4ab
We know ab = 10
Thus, 4ab = 4(10) = 40
∴ (a + b)² - (a - b)² = 40

[jgoemat]

Since it holds true for all ab=10, I just picked 5 and 2 and got 49 - 9 = 40

[sparkyheberling]

It's simpler to factor it as the difference of squares:
(a+b)² - (a-b)²
= [(a+b)+(a-b)] × [(a+b)-(a-b))]
= [2a] × [2b]
= 4ab
= 40

[worldwidedatarht]

SIR, AMAZING!!!
YOU ARE REALLY A INTELLIGENT!!!

[kunalghosh]

Actually 90% of people get this right😅... If they studied at class 8😅

[status]

been so long since I've done this that I thought we gonna end up with a^2-b^2

[rattanversha]

An another is: is let x=a+b, and y=a-b
By substituting the values In the 1 equation
We get
X²-y²=(x+y)(x-y) Putting the values of x and y
(a+b+a-b)[ a+b-(a-b)]
(2a)(a+b-a+b)
2a×2b=4ab= 4×10=40

[thexraptor]

You could use this method or if you were unsure on a test you could just use the method that always works though takes a bit more time, brute forcing. Take 2 numbers who’s product is 10 and plug them in ex. 10 and 1; or 5 and 2 and plug them in and solve.

Most of the SAT questions are like this, most likely purposefully. It’s not trying to see if you know the method to doing the problem, but actually knowing how to, using basic math principles, make a problem that you wouldn’t know how to do into something that you can do using logical thinking. That’s why you don’t see advanced Calculus or Physics based questions on the SAT because you may need to know a certain way of how to do the problem to actually do it. There’s no thinking or problem solving in that. It’s either you know it or you don’t and that is not what the SAT is trying to test at all. Hopefully this clears up some confusion as to why the SAT usually has easier problems than what you may see on a college entrance exam, etc.

[SgtEnder]

I did difference of two squares instead.
((a+b)+(a-b))((a+b)-(a-b)) =
2a * 2b =
4ab = 40

[No_One_Special]

Could also solve as difference of two squares:

((a+b)+(a-b))*((a+b)-(a-b))
(2a)(2b)
4ab
40

[lakshmanayb]

Wow Nice .. To easily understanding this method by using formula ... Tqsm sir

[shines-]

(a+b)^2-(a-b)^2= a squared+ 2ab+ b squared -a squared +2ab-b squared =4ab=4*10=40

[Labrador.]

A lot of you aren’t understanding the quantity of problems there are in the sat, this should be automatic

[shohomchakraborty]

American high schooler here. This is hella easy, yes, but that’s kind of the point. The SAT is not hard at all, given enough time even the most average students in high school could get a near-perfect score. However, the SAT is not a test of your knowledge (they don’t go beyond 10th grade math level due to lack of a unified and standardized math curriculum across the country), it is a test of your ability to answer questions as quickly and efficiently as possible. Colleges see high SAT scores as a sign that the students themselves are capable of handling the rigor and fast pace of standardized tests within universities.

[ahnickcoverreactionchannel]

(a + b)^2 - (a - b)^2
= (a+b+a-b)(a+b-a+b)
= (2a)(2b)
= 4ab
= 4 x 10
= 40

difference of two squares formula

[ompatnaik]

this is how i did it,
If we use identity a^2 - b^2 = (a+b)(a-b)
a= (a+b) b=(a-b)
[(a+b)+(a-b)][(a+b)-(a-b)]
- (2a)(2b)
- 4ab
-40

[atilanorodriguez]

Just use 5 and 2 for a and b respectively, then do the math.
Way easier and you don't have to know how to expand binomials.

[littledevilgaming]

Difference of two squares is an alternative method to solving this question
Because x^2 - y^2 = (x+y)(x-y)
We can rewrite this as
(a+b+a-b)(a+b-(a-b))
(2a)(2b)
4ab
4(10)
40

[saw]

Just as a note, if you are attempting to break something down... just saying FOIL doesn't help.

It took me quite a while to figure out that you broke down the exponent into A+B (a+b). If you're going to teach, you gotta show every step and not jump into the middle

[ploppy]

I did this problem differently, I used difference of squares. I did:
(a+b+(a-b))(a+b-(a-b))=
(2a)(2b)=
4ab