中二升中三英數help?

1.Expand [2x+(3y-2)][2x-(3y-2)]by using identity.

Let A = 2x
and B = (3y-2)

then you get (A+B)(A-B) = (A^2 - B^2)

so [2x+(3y-2)][2x-(3y-2)] = [(2x)^2 - (3y-2)^2]
= 4x^2 - (9y^2 + 4 - 12y)
= 4x^2 - 9y^2 - 4 + 12y

2.Expand (a+b+c+d)(a+b-c-d).
This is the same as the last one,

Let X = a+b
and Y = c+d

(a+b+c+d)(a+b-c-d) = [(a+b)+(c+d)][(a+b)-(c+d)] = [X+Y][X-Y]
= X^2 - Y^2
= (a+b)^2 - (c+d)^2
= a^2 + b^2 + 2ab - (c^2 + d^2 + 2cd)
= a^2 + b^2 + 2ab - c^2 - d^2 - 2cd

3.Two simultaneous linear equations in two unknowns have0,1 or infinite
number of solutions.How do we know that?State your reasoning.

A linear equation with two unknowns can be expressed as a line on the Cartesian plane (or x-y plane). When there are two lines intercept on the Cartesian plane, it means that the x,y coordinates satisfy both linear equation at the same time or in other word, this x,y value is a solution to this two linear equations simultaneously.

There are three different scenario in how this two lines meet. They are intercept each other at one point, or one overlap the other, or they don't meet at all as they are parallel to one another.

When the two lines intercept each other at one point, it means there is only one x,y value that is a solution to this two linear equations simultaneously.

When the two lines overlap one another, it means for any x,y on one line is a solution to the other line, therefore, there are infinite number of solution.

When the two lines do not intercept at all. It means that there are no x,y value that satify both linear equation at the same time, thus there are no solutions.