What is the factored form of the following expression? x2 – 4xy – 21y2
(x-7y)(x+3y)
^^^^^^just it's backwards (x + 3)(x - 7y)
To factor the expression x^2 - 4xy - 21y^2, we can use the fact that it is a quadratic expression in two variables.
Step 1: We need to find pairs of numbers that multiply to give -21y^2 and add up to -4xy.
The pairs that multiply to give -21y^2 are (-y, 21y) and (y, -21y).
The pairs that add up to -4xy are (-3x, -7x) and (3x, 7x).
Step 2: Now we need to rearrange the terms in the expression using these pairs of numbers.
We can rewrite the expression as:
(x^2 - 7xy) + (-3xy - 21y^2)
Step 3: Now we can factor out common terms from each group.
In the first group, we can factor out "x" to get:
x(x - 7y)
In the second group, we can factor out "-3y" to get:
-3y(x + 7y)
Step 4: Putting it all together, the factored form of the expression x^2 - 4xy - 21y^2 is:
(x - 7y)(x + 3y)
So, the factored form of the expression is (x - 7y)(x + 3y).
To find the factored form of the expression x^2 - 4xy - 21y^2, we can use the method of factoring by grouping.
Step 1: Split the middle term -4xy into two terms such that their coefficients multiply to give -21 (the coefficient of y^2) and -4xy.
The factors of -21 that multiply to -4 are -7 and 3. So we can rewrite -4xy as -7xy + 3xy.
Now, the expression becomes: x^2 - 7xy + 3xy - 21y^2.
Step 2: Group the terms and factor them separately:
(x^2 - 7xy) + (3xy - 21y^2).
Factoring out the greatest common factor from each group:
x(x - 7y) + 3y(x - 7y).
Step 3: Notice that we have a common binomial factor, (x - 7y), in both terms. We can factor it out:
(x - 7y)(x + 3y).
Therefore, the factored form of the expression x^2 - 4xy - 21y^2 is (x - 7y)(x + 3y).