A level Maths question

Hi everyone. I was wondering if anyone could help me answer this question. The mark scheme just shows an answer but I don’t know how to get there.
Show how binomial expansion can be used to solve the following without a calculator:
A: (268^2)-(232^2)
B: (65.1*29.2+35.9*65.1-26.4*91.7+26.4*65.3)/(18.3^2 -18.3*5.4)

Any help would be amazing.

Hi everyone. I was wondering if anyone could help me answer this question. The mark scheme just shows an answer but I don’t know how to get there.
Show how binomial expansion can be used to solve the following without a calculator:
A: (268^2)-(232^2)
B: (65.1*29.2+35.9*65.1-26.4*91.7+26.4*65.3)/(18.3^2 -18.3*5.4)

Any help would be amazing.

Hi everyone. I was wondering if anyone could help me answer this question. The mark scheme just shows an answer but I don’t know how to get there.
Show how binomial expansion can be used to solve the following without a calculator:
A: (268^2)-(232^2)
B: (65.1*29.2+35.9*65.1-26.4*91.7+26.4*65.3)/(18.3^2 -18.3*5.4)

Any help would be amazing.

A - you have a difference of two squares (hint)

No, although you are right, you won't be accurate in this situation since it was asked to make use of binomial expansion.

For part B) It can be written as <redacted> and use binomial expansion to simplify further

Of course it will be accurate - it's an exact method.

Tbf, its what the question asked for, though its less obvious than just dots. For the OP the question is asking about inverse of babylonian multiplication
https://math.widulski.net/worksheets/BabylonianMultiplication.html
so evaulate 4ab rather than (a+b)^2 - (a-b)^2. Though obv dots/simple factorisation is easier to simply spot and gives the "same" 4ab term.

Partially because I see no point in making life difficult, I would claim here that since technically, (a-b) and (a+b) are binomial terms, (a-b)(a+b) = a^2-b^2 is a binomial expansion.