How do you simplify #(5 + 2sqrt2)(8 - 3sqrt2)#?

Answer 1

See a solution process below:

To multiply and simplify these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

#(color(red)(5) + color(red)(2sqrt(2)))(color(blue)(8) - color(blue)(3sqrt(2)))# becomes:
#(color(red)(5) xx color(blue)(8)) - (color(red)(5) xx color(blue)(3sqrt(2))) + (color(red)(2sqrt(2)) xx color(blue)(8)) - (color(red)(2sqrt(2)) xx color(blue)(3sqrt(2)))#
#40 - 15sqrt(2) + 16sqrt(2) - 6(sqrt(2))^2#
#40 + (-15 + 16)sqrt(2) - (6 xx 2)#
#40 + 1sqrt(2) - 12#
#40 + sqrt(2) - 12#
#40 - 12 + sqrt(2)#
#28 + sqrt(2)#
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Answer 2

To simplify the expression (5 + 2sqrt2)(8 - 3sqrt2), you can use the distributive property. Multiply each term in the first expression by each term in the second expression, and then combine like terms. The simplified expression is 40 - 15sqrt2 + 16sqrt2 - 6(2). Simplifying further, the expression simplifies to 40 + sqrt2.

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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.

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.

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.

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.

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