Radicals and the Foil Method

1/31/2011

How do you multiply these:
(9 + √10)(9 - √10)

Use the foil method when multiplying two binomials.
(9 + √10)(9 - √10)
= 9(9) + 9(-√10) + √10(9) + √10(-√10) {used foil method}
= 81 - 9√10 + 9√10 - √100 {multiplied through}
= 81 - √100 {combined like terms}
= 81 - 10 {evaluated square root of 100 to be 10}
= 71

- Algebra House

2 Comments

Muhsin

1/31/2011 12:11:54 am

Can we use diffenrence of 2 squares ?

Algebra House

1/31/2011 03:10:37 am

Yes, as with many problems, there are other ways to work this.

You could use the "sum and difference pattern", which equals a "difference of two squares"

Sum and Difference Pattern:
(a + b)(a - b) = a^2 - b^2

(9 + √10)(9 - √10)
= (9)^2 - [√10]^2
= 81 - 10
= 71

Same answer....different method.

Thanks for your input!

- Algebra House

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