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How do you simplify #(1-sqrt3) (3+ sqrt2)#?

Answer 1

Abigail Allen

#3+sqrt2-3sqrt3-sqrt6#

Use the FOIL method of multiplying Binomials:

#(1-sqrt3)(3+sqrt2)#

#ul Firsts#

#rarr=1*3=3#

#ul Outer#

#rarr=1*sqrt2=sqrt2#

#ul I##n##n##er#

#rarr=-sqrt3*3=-3sqrt3#

#ul L##a##st#

#rarr=-sqrt3*sqrt2=-sqrt6#

Now put them all together:

#(1-sqrt3)(3+sqrt2)=3+sqrt2-3sqrt3-sqrt6#

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Answer 2

Jace Anderson

To simplify the expression (1 - √3)(3 + √2), we can use the distributive property of multiplication.

First, multiply 1 by each term inside the second parentheses: 1 * 3 = 3 and 1 * √2 = √2.

Next, multiply -√3 by each term inside the second parentheses: -√3 * 3 = -3√3 and -√3 * √2 = -√6.

Now, we have four terms: 3, √2, -3√3, and -√6.

Combining like terms, we have 3 - 3√3 + √2 - √6.

This is the simplified form of (1 - √3)(3 + √2).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.