What is the coefficient of x² here

Find the coefficient of x² in the binomial expansion of (2-5x)(1+2x)^7

You don't have to multiply the whole thing out.

Here are the ways to get x^2:
- constant term in (2 - 5x) times the x^2 term in (1 + 2x)^7
- x term in (2 - 5x) times the x term in (1 + 2x)^7

and that's it. So you just have to figure those two terms.
The x^2 term in (1 + 2x)^7 is 7C2 * (2x)^2 * 1^5 = 21 * 4x * 1 = 84x
2 * 84x = 168x

The x term in (1 + 2x)^7 is 7C1 * (2x)^1 * 1^6 = 7 * 2x * 1 = 14x.
-5x * 14x = -70x

Add those up for your answer.

when you multiply this out it becomes

-640 x^8-1984 x^7-2464 x^6-1456 x^5-280 x^4+140 x^3+98 x^2+23 x+2

so 98 is the coefficient of x^2