MULTIPLYING BINOMIALS WITH RADICALS

Expand and simplify :

Problem 1 :

(4 + √3) (4 - √3)

Solution :

(4 + √3) (4 - √3)

= 4(4) - 4√3 + 4√3 - (√3)²

= 16 - 3

= 13

Problem 2 :

(5 - √2) (5 + √2)

Solution :

(5 - √2) (5 + √2)

= 5(5) + 5√2 - 5√2 - (√2)²

= 25 - 2

= 23

Problem 3 :

(√5 - 2 ) (√5 + 2)

Solution :

(√5 - 2) (√5 + 2)

= (√5)² + 2√5 - 2√5 - 4

= 5 - 4

= 1

Problem 4 :

(√7 + 4 ) (√7 - 4)

Solution :

(√7 + 4) (√7 - 4)

= (√7)² - 4√7 + 4√7 - 16

= 7 - 16

= -9

Problem 5 :

(3√2 + 2 ) (3√2 - 2)

Solution :

(3√2 + 2) (3√2 - 2)

= 3²(√2)² - 6√2 + 6√2 - 4

= 18 - 4

= 14

Problem 6 :

(2√5 - 1 ) (2√5 + 1)

Solution :

(2√5 - 1) (2√5 + 1)

= 2²(√5)² + 2√5 - 2√5 - 1

= 20 - 1

= 19

Problem 7 :

(5 - 3√3) (5 + 3√3)

Solution :

(5 - 3√3) (5 + 3√3)

= 5(5) + 15√3 - 15√3 - 9(√3)²

= 25 - 27

= -2

Problem 8 :

(2 - 4√2) (2 + 4√2)

Solution :

(2 - 4√2) (2 + 4√2)

= 2(2) + 8√2 - 8√2 - 16(√2)²

= 4 - 32

= -28

Problem 9 :

(1 + 5√7) (1 - 5√7)

Solution :

(1 + 5√7) (1 - 5√7)

= 1(1) - 5√7 + 5√7 - 25(√7)²

= 1 - 175

= -174