Question

Simplify (x + y + 3)(x + y - 4)

Answer 1

x²+2xy-x+y²-y-12

Explanation:

(x+y+3)(x+y-4)

= x(x+y-4)+y(x+y-4)+3(x+y-4)

= x²+xy-4x+xy+y²-4y+3x+3y-12

= x²+2xy-x+y²-y-12

Answer 2

Hello!

The answer is:

The simplified expression is:

`(x + y + 3)(x + y - 4)=x^(2) +y^(2) +2xy-x-y-12`

Why?

To solve the problem, we need to remember how to use the distributive property and how to add like terms.

The distributive property can be defined as follow:

`(a+b)(c+d)=ab+ad+bc+bd`

The like terms are the terms that share the same variable and the same exponent, for example:

`3x+x+ x^(2)=x^(2) +4x`

We were able to add the first and the second term because they share the same variable and the same exponent.

Now, we are given the expression:

`(x+y+3)(x+y-4)`

So, simplifying we have:

`(x + y + 3)(x + y - 4)=(x*x)+(x*y)-(4*x)+(y*x)+(y*y)-(4*y)+(3*x)+(3*y)-(3*4)\\\\(x + y + 3)(x + y - 4)=x^(2) +xy-4x+xy+y^(2)-4y+3x+3y-12\\\\(x + y + 3)(x + y - 4)=x^(2) +y^(2) +2xy-x-y-12`

Hence, we have that the simplified expression is:

`(x + y + 3)(x + y - 4)=x^(2) +y^(2) +2xy-x-y-12`

Have a nice day!