Can (-x – y) (x + y) be multiplied by using the difference-of-squares formula? Explain why or why not
No it cannot because it is different from the difference of the squares formula i.e. (X-Y)(X+Y)
for this, it becomes -(x+y)(x+y) = -(x+y)^2 which is different from the difference of squares identity
No, (-x - y)(x + y) cannot be multiplied using the difference-of-squares formula.
The difference-of-squares formula is specifically used to multiply two expressions of the form (a - b)(a + b), where a and b are variables or constants. In this case, we have (-x - y)(x + y), which does not fit the form of the difference-of-squares formula because the signs in front of x and y are different (-x and +x).
To multiply (-x - y)(x + y), you would need to use the distributive property, which states that the product of two binomials can be found by multiplying each term of one binomial by each term of the other binomial and then combining like terms.
To determine if the expression (-x - y)(x + y) can be multiplied using the difference-of-squares formula, we first need to understand what the difference-of-squares formula is.
The difference-of-squares formula states that for any two numbers a and b, the product of their sum and difference is equal to the difference of their squares. Mathematically, it can be expressed as:
(a + b)(a - b) = a^2 - b^2
Now let's apply this formula to the expression (-x - y)(x + y) and see if it matches the difference-of-squares form.
Expanding the expression, we get:
(-x - y)(x + y) = -x(x) + x(y) - y(x) - y(y)
= -x^2 + xy - xy - y^2
= -x^2 - y^2
We can see that the expression -x^2 - y^2 does not match the difference-of-squares form a^2 - b^2. The expression is a sum of two squared terms, rather than a difference. Therefore, we cannot use the difference-of-squares formula to multiply (-x - y)(x + y).
In summary, the expression (-x - y)(x + y) cannot be multiplied using the difference-of-squares formula because it does not meet the requirements of a difference between squares.