Questions: Find the product. [ (x^7 y^4-5)^2 ]

Solution Steps

We start with the expression \((x^{7} y^{4} - 5)^{2}\).

Using the binomial expansion formula \((a - b)^{2} = a^{2} - 2ab + b^{2}\), we identify \(a = x^{7} y^{4}\) and \(b = 5\). Thus, we can expand the expression as follows: \[ (x^{7} y^{4})^{2} - 2(x^{7} y^{4})(5) + 5^{2} \]

Calculating each term gives us:

• The first term: \((x^{7} y^{4})^{2} = x^{14} y^{8}\)
• The second term: \(-2(x^{7} y^{4})(5) = -10 x^{7} y^{4}\)
• The third term: \(5^{2} = 25\)

Combining these results, we have: \[ x^{14} y^{8} - 10 x^{7} y^{4} + 25 \]

Thus, the simplified expression is: \[ (x^{7} y^{4} - 5)^{2} = x^{14} y^{8} - 10 x^{7} y^{4} + 25 \]

Final Answer