Question

Simplify the expression: px^2 - py^2 - qx^2 - qy^2.

A. p(x+y)(x-y) - q(x+y)(x-y)
B. (p-q)(x^2-y^2)
C. (p+q)(x+y)(x-y)
D. px(x-y) - qy(x+y)

Answer 1

The expression px^2 - py^2 - qx^2 - qy^2 can be simplified to (p-q)(x^2-y^2) by factoring out common terms and using the difference of squares formula, resulting in option B.

Therefore, the correct answer is option B. (p-q)(x^2-y^2).

Step-by-step explanation:

The expression provided by the student is px^2 - py^2 - qx^2 - qy^2. This expression can be simplified by factoring out common terms and using the difference of squares formula. The difference of squares formula states that a^2 - b^2 = (a + b)(a - b). To apply this to the given expression, we can factor out 'p' from the first two terms and factor out '-q' from the last two terms, which would give us:

p(x^2 - y^2) - q(x^2 - y^2)

We can now factor (x^2 - y^2) as (x + y)(x - y), but since it is common to both terms with 'p' and 'q', we can combine them to get:

(p - q)(x + y)(x - y)

However, since we are not given an option with (x + y)(x - y), we can leave it in the factored form of x^2 - y^2, which results in the correct simplified form:

(p - q)(x^2 - y^2)

Therefore, the correct answer is option B. (p-q)(x^2-y^2).