Question

Factor the expression​

Answer 1

The factored form of the expression
`\(x^2 - 3xy - 33y^2\)` is
`\((x - 11y)(x + 3y)\).`

To factor the expression
`\(x^2 - 3xy - 33y^2\)`, we need to find two binomials whose product is equal to the given expression.

The general form of the quadratic expression
`\(ax^2 + bx + c\)` can be factored into
`\((px + q)(rx + s)\)`, where p, q, r, and s are constants. In this case, we have:

`\[x^2 - 3xy - 33y^2\]`

To factor this expression, we need to find two values m and n such that:

`\[mn = ac = (1)(-33) = -33\]`

m + n = b = -3

The values m and n that satisfy these conditions are m = 11 and n = -3. Now, we can factor the expression:

`\[x^2 - 3xy - 33y^2 = (x - 11y)(x + 3y)\]`

So, the factored form of the expression
`\(x^2 - 3xy - 33y^2\)` is
`\((x - 11y)(x + 3y)\).`