Explanation:
The product of the form method is a technique used to factorize a quadratic expression of the form ax^2 + bx + c. Here are the steps to follow:
1. Write down the quadratic expression in the standard form ax^2 + bx + c, where a, b, and c are constants.
2. Multiply the coefficient a by the constant c to get the product ac.
3. Find two factors of ac that add up to the coefficient b. In other words, find two numbers p and q such that pq = ac and p + q = b.
4. Rewrite the quadratic expression by replacing the middle term bx with the two terms px and qx. This is done by splitting the middle term of the quadratic expression using the two numbers p and q found in step 3. So the quadratic expression becomes ax^2 + px + qx + c.
5. Factor the first two terms of the expression ax^2 + px using the greatest common factor (GCF). This gives us a(x + p/a)x + qx + c.
6. Factor the last two terms qx + c using the GCF. This gives us a(x + p/a)(x + c/q).
7. Simplify the expression by combining any like terms and check that the factors obtained in step 6 can be expanded back into the original quadratic expression.
8. Write down the factored form of the quadratic expression, which is (x + p/a)(x + c/q).
These are the steps of the product of the form method.