Question

thursday: 1 - 15 - 26
① $25n^3 - 20n^2 - 20n + 16 =$
② $7k^3 - 56^2k - 3k + 24 =$

Explanation:

Problem 1: Factor \(25n^3 - 20n^2 - 20n + 16\)

Step 1: Group Terms

Group the first two terms and the last two terms:
\((25n^3 - 20n^2) + (-20n + 16)\)

Step 2: Factor Out GCF from Each Group

Factor out \(5n^2\) from the first group and \(-4\) from the second group:
\(5n^2(5n - 4) - 4(5n - 4)\)

Step 3: Factor Out Common Binomial

Factor out \((5n - 4)\) from both terms:
\((5n - 4)(5n^2 - 4)\)

Step 1: Correct the Expression (Assumption)

Assume the expression is \(7k^3 - 56k^2 - 3k + 24\) (correcting \(56^2k\) to \(56k^2\)). Group terms:
\((7k^3 - 56k^2) + (-3k + 24)\)

Step 2: Factor Out GCF from Each Group

Factor out \(7k^2\) from the first group and \(-3\) from the second group:
\(7k^2(k - 8) - 3(k - 8)\)

Step 3: Factor Out Common Binomial

Factor out \((k - 8)\) from both terms:
\((k - 8)(7k^2 - 3)\)

Answer:

\(\boldsymbol{(5n - 4)(5n^2 - 4)}\)

Problem 2: Factor \(7k^3 - 56^2k - 3k + 24\) (Assuming \(56^2k\) is a typo, likely \(56k^2\))