Factorise 8a^2 - 50b^2 completely.

In this expression the student must recognise the form is typical of a difference of squares situation (when you have two terms squared and a minus sign between them). This means the factorisation will be two expressions in brackets, one with a plus sign and the other with a minus sign, so something like this:

(4a + 10b)(2a - 5b)

You can further factorise a 2 out of the first brackets to get:

2(2a + 5b)(2a - 5b)

And now you cannot factorise further so the factorisation is complete.

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