Given, x + 8 x - 10 Using the identity, x + a x + b = x 2 + a + b x + a b x + 8 x + 10 = x 2 + 8 - 10 x + 8 × - 10 = x 2 - 2 x - 80

Given, x - 8 x + 10 Using the identity, x + a x + b = x 2 + a + b x + a b x + 8 x + 10 = x 2 + - 8 + 10 x + - 8 × 10 = x 2 + 2 x - 80

Given, x - 8 x - 10 Using the identity, x + a x + b = x 2 + a + b x + a b x - 8 x - 10 = x 2 + - 8 - 10 x + - 8 × - 10 = x 2 - 18 x + 80

Expand 2 x - 1 x 3 x + 2 x

Given, 2 x - 1 x 3 x + 2 x When multiplying a binomial times a binomial, each term of the first binomial must be multiplied by each term of the second binomial Here, 2 x - 1 x 3 x + 2 x = 2 x 3 x + 2 x - 1 x 3 x + 2 x = 6 x 2 + 4 - 3 - 2 x 2 = 6 x 2 - 2 x 2 + 1

Expand 3 a + 2 b 2 a - 3 b

Given, 3 a + 2 b 2 a - 3 b When multiplying a binomial times a binomial, each term of the first binomial must be multiplied by each term of the second binomial Here, 3 a + 2 b 2 a - 3 b = 3 a 2 a - 3 b + 2 b 2 a - 3 b = 6 a 2 - 9 a b + 4 a b - 6 b 2 = 6 a 2 - 5 a b - 6 b 2

Given: x + y - z 2 Expanding using algebraic identity, a + b + c 2 = a 2 + b 2 + c 2 + 2 a b + b c + 2 a c Here, a = x , b = y , c = - z x + y - z 2 = x + y + - z 2 = ( x ) 2 + ( y ) 2 + ( - z ) 2 + 2 × x ( y ) + 2 × ( y ) ( - z ) + 2 ( - z ) × x = x 2 + y 2 + z 2 + 2 x y - 2 y z - 2 x z

Given: x - 2 y + z 2 Expanding using algebraic identity, a + b + c 2 = a 2 + b 2 + c 2 + 2 a b + b c + 2 a c Here, a = x , b = - 2 y , c = z x + y - z 2 = x + - 2 y + z 2 = ( x ) 2 + ( - 2 y ) 2 + ( z ) 2 + 2 × x ( - 2 y ) + 2 × ( - 2 y ) ( z ) + 2 ( z ) × x = x 2 + 4 y 2 + z 2 - 4 x y - 4 y z + 2 x z