The first step is to consider the polynomial 16n⁸ -24n⁴p - 7p², which we aim to factorize.
Factorizing a polynomial is the process of breaking it down into its simplest factors, which when multiplied together, yield the original polynomial.
Here's the step by step process for our equation:
Step 1: Look for common factors if any, in this case, there are none.
Step 2: Identify whether the polynomial can be factored by grouping. The equation 16n⁸ -24n⁴p - 7p² is a polynomial of the form ax⁴ + bxy + cy². When it is a trinomial and of this particular form, the factorization can be written in the form (dx² + ey)(fx² - gy), where d, e, f, and g are the coefficients obtained from the factorization.
Step 3: Now we group terms and factor the result. Looking at the equation you can group the terms to (16n⁸ - 24n⁴p) and (-7p²).
Step 4: Now we need to find the products. In our case, the grouping of equation results in two factors (-4n⁴ + 7p) and (4n⁴ + p).
Step 5: The completely factored form is the product of these two binomials, in other words, the factored form of the equation will be -(-4n⁴ + 7p)*(4n⁴ + p).
So, the original equation 16n⁸ -24n⁴p - 7p² factors to -(-4n⁴ + 7p)*(4n⁴ + p).