Math  /  Algebra

QuestionQUESTION 2 Multiply and simplify completely. (26)(4+6)(2-\sqrt{6})(4+\sqrt{6}) \square

Studdy Solution

STEP 1

1. We need to multiply two binomials.
2. The expression can be simplified using the distributive property (also known as the FOIL method for binomials).

STEP 2

1. Apply the distributive property to multiply the binomials.
2. Simplify the resulting expression by combining like terms.

STEP 3

Apply the distributive property (FOIL method) to multiply the binomials (26)(2-\sqrt{6}) and (4+6)(4+\sqrt{6}).
First, multiply the first terms: 2×4=8 2 \times 4 = 8
Outer, multiply the outer terms: 2×6=26 2 \times \sqrt{6} = 2\sqrt{6}
Inner, multiply the inner terms: 6×4=46 -\sqrt{6} \times 4 = -4\sqrt{6}
Last, multiply the last terms: 6×6=(6)2=6 -\sqrt{6} \times \sqrt{6} = -(\sqrt{6})^2 = -6

STEP 4

Combine all the results from the multiplication:
8+26466 8 + 2\sqrt{6} - 4\sqrt{6} - 6

STEP 5

Simplify the expression by combining like terms:
Combine the constant terms: 86=2 8 - 6 = 2
Combine the radical terms: 2646=26 2\sqrt{6} - 4\sqrt{6} = -2\sqrt{6}
So, the simplified expression is: 226 2 - 2\sqrt{6}
The simplified expression is: 226 \boxed{2 - 2\sqrt{6}}

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