Questions: Perform the indicated operation. [ (-5+10 sqrt11)(6+6 sqrt11) ]

Solution Steps

To solve the given expression, we need to apply the distributive property (also known as the FOIL method for binomials) to multiply the two binomials. This involves multiplying each term in the first binomial by each term in the second binomial and then combining like terms.

We start with the expression \((-5 + 10\sqrt{11})(6 + 6\sqrt{11})\).

Using the distributive property, we expand the expression: \[ (-5)(6) + (-5)(6\sqrt{11}) + (10\sqrt{11})(6) + (10\sqrt{11})(6\sqrt{11}) \]

Calculating each term gives us:

• First term: \(-5 \cdot 6 = -30\)
• Second term: \(-5 \cdot 6\sqrt{11} = -30\sqrt{11}\)
• Third term: \(10\sqrt{11} \cdot 6 = 60\sqrt{11}\)
• Fourth term: \(10\sqrt{11} \cdot 6\sqrt{11} = 60 \cdot 11 = 660\)

Now we combine the like terms: \[ -30 + 660 + (-30\sqrt{11} + 60\sqrt{11}) = 630 + 30\sqrt{11} \]

Final Answer