Simplify Binomial Surd Expressions using the FOIL Method 1

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Question 1 of 3

Simplify

`(sqrt2+3) (sqrt2-4)`

Question 2 of 3

Simplify

`(3sqrt2-sqrt6) (2sqrt2+3sqrt6)`

Question 3 of 3

Simplify

`(sqrt7-5sqrt2) (sqrt2-5sqrt7)`

`=`	`(color(darkviolet)(sqrt2)+color(royalblue)(3)) (color(forestgreen)(sqrt2)-color(crimson)(4))`
`=`	`color(darkviolet)(sqrt2) xx color(forestgreen)(sqrt2)-color(darkviolet)(sqrt2) xx color(crimson)(4)+color(royalblue)(3) xx color(forestgreen)(sqrt2)-color(royalblue)(3)color(crimson)(4)`
`=`	`sqrt4 – 4sqrt2 + 3sqrt2 – 12`	Simplify like terms (same radicand)
`=`	`2 – sqrt2 – 12`	Simplify like terms (constants)
`=`	`- sqrt2 – 10`

`=`	`(color(darkviolet)(3sqrt2)-color(royalblue)(sqrt6)) (color(forestgreen)(2sqrt2)+color(crimson)(3sqrt6))`
`=`	`color(darkviolet)(3sqrt2) xx color(forestgreen)(2sqrt2)+color(darkviolet)(3sqrt2) xx color(crimson)(3sqrt6)-color(royalblue)(sqrt6) xx color(forestgreen)(sqrt2)-color(royalblue)(sqrt6) xx color(crimson)(3sqrt6)`
`=`	`6sqrt4 + 9sqrt12 -2sqrt12-3sqrt36`	Simplify the Surds
`=`	`6 xx 2 + 9 xx 2sqrt3 – 2 xx 2sqrt3 – 3 xx 6`	Multiplying
`=`	`12 + 18sqrt3-4sqrt3-18`	Combine like Terms
`=`	`14sqrt3- 6`

`=`	`(color(darkviolet)(sqrt7)-color(royalblue)(5sqrt2)) (color(forestgreen)(sqrt2)-color(crimson)(5sqrt7))`
`=`	`color(darkviolet)(sqrt7) xx color(forestgreen)(sqrt2)-color(darkviolet)(sqrt7) xx color(crimson)(5sqrt7)-color(royalblue)(5sqrt2) xx color(forestgreen)(sqrt2)+color(royalblue)(5sqrt2) xx color(crimson)(5sqrt7)`
`=`	`sqrt14 – 5sqrt49 – 5sqrt4 + 25sqrt14`	Simplify the Surds
`=`	`sqrt14 – 5 xx 7- 5 xx 2 + 25sqrt14`	Multiplying
`=`	`sqrt14 – 35- 10 + 25sqrt14`	Combine like Terms
`=`	`26sqrt14- 45`