This should be a Sec 2 topic rather than a Sec 1 topic, since Sec 1 students only learn linear expressions (unless you are ahead of the pack or you decide that it's still 2021 so you are still Sec 1.

When we say expand here, we mean multiplying the terms in, rather than increasing the spacing between each symbol. I mean, (x - y)² does not become ( x - y ) ².

Give me a moment to write down.

this is my sec 2 tuition homework i forgot to change from sec 1 to sec 2 sorry

Let's expand (x - y)² algebraically.

Have you learnt the "rainbow expansion" or equivalent? Something like 5 (x + 2) = 5x + 10.

If you have, then it works similarly here.

(x - y)²
= (x - y) (x - y)
= xx - xy - yx + yy (two negatives multiplied together make a positive)
= x² - xy - xy + y² (x times x is written as x²; xy and yx are the same thing)
= x² - 2xy + y² (yes, -xy - xy becomes -2xy)
= x² + y² - 2xy

The expansion process has been done. Let's now solve the question

(x - y)² = 50
x² + y² - 2xy = 50

Because we are given that xy = 7,
x² + y² - 2 (7) = 50
x² + y² - 14 = 50
x² + y² = 50 + 14
x² + y² = 64

Done! We are not required to find individual values of x and y in solving this.

what about the second question?

Similarly (I will cut the working shorter this time),

(x + y)²
= (x + y) (x + y)
= x² + xy + yx + y²
= x² + 2xy + y²
= x² + y² + 2xy

Let's put them into the equation.

(x + y)² = 63
x² + y² + 2xy = 63

Since xy = 5.5,
x² + y² + 2 (5.5) = 63
x² + y² + 11 = 63
x² + y² = 63 - 11
x² + y² = 52

We just need to subtract 1 here.

x² + y² - 1 = 52 - 1
x² + y² - 1 = 51

You need time to allow me to post the answers one by one. It would take me a longer time to type everything in a single go. Also, writing everything in a single go runs the risk of me losing all my written text (because it has happened before).

alright im sorry and thanks for the help