Simplify the following. 1 2 x 3 y 3 - z 3 + 1 2 y 3 z 3 - x 3 + 1 2 z 3 x 3 - y 3

Given, 1 2 x 3 y 3 - z 3 + 1 2 y 3 z 3 - x 3 + 1 2 z 3 x 3 - y 3 A binomial is defined as an algebraic expression that has two terms connected by a plus or a minus sign. Multiplying binomials is similar to the multiplication of two whole numbers or fractions. Thus, ⇒ 1 2 x 3 y 3 - z 3 + 1 2 y 3 z 3 - x 3 + 1 2 z 3 x 3 - y 3 = 1 2 x 3 y 3 - 1 2 x 3 z 3 + 1 2 y 3 z 3 - 1 2 y 3 x 3 + 1 2 z 3 x 3 - 1 2 z 3 y 3 = 0 Hence, the required answer is obtained.

Simplify the following. 1 2 x 3 y 3 - z 3 + 1 2 y 3 z 3 - x 3 + 1 2 z 3 x 3 - y 3

Given, 1 2 x 3 y 3 - z 3 + 1 2 y 3 z 3 - x 3 + 1 2 z 3 x 3 - y 3 A binomial is defined as an algebraic expression that has two terms connected by a plus or a minus sign. Multiplying binomials is similar to the multiplication of two whole numbers or fractions. Thus, ⇒ 1 2 x 3 y 3 - z 3 + 1 2 y 3 z 3 - x 3 + 1 2 z 3 x 3 - y 3 = 1 2 x 3 y 3 - 1 2 x 3 z 3 + 1 2 y 3 z 3 - 1 2 y 3 x 3 + 1 2 z 3 x 3 - 1 2 z 3 y 3 = 0 Hence, the required answer is obtained.

Simplify the following. 3 2 x 2 1 3 - x 2 + 3 x 1 2 x 3 - 1 3 x + 9 5 x 2 x 3 - x

Given, 3 2 x 2 1 3 - x 2 + 3 x 1 2 x 3 - 1 3 x + 9 5 x 2 x 3 - x A binomial is defined as an algebraic expression that has two terms connected by a plus or a minus sign. Multiplying binomials is similar to the multiplication of two whole numbers or fractions. Thus, ⇒ 3 2 x 2 1 3 - x 2 + 3 x 1 2 x 3 - 1 3 x + 9 5 x 2 x 3 - x = 3 2 × 1 3 x 2 - 3 2 x 4 + 3 2 x 4 - 1 x 2 + 9 5 x 5 - 9 5 x 3 = 9 5 x 5 - 9 5 x 3 - x 2 2 Hence, the required answer is obtained.

Simplify the following. 1 3 x x 2 - x 3 + 2 3 x 2 x 3 - x + 4 3 x 3 x - x 2

Given, 1 3 x x 2 - x 3 + 2 3 x 2 x 3 - x + 4 3 x 3 x - x 2 A binomial is defined as an algebraic expression that has two terms connected by a plus or a minus sign. Multiplying binomials is similar to the multiplication of two whole numbers or fractions. Thus, ⇒ 1 3 x x 2 - x 3 + 2 3 x 2 x 3 - x + 4 3 x 3 x - x 2 = 1 3 x 3 - 1 3 x 4 + 2 3 x 5 - 2 3 x 3 + 4 3 x 4 - 4 3 x 5 = 1 3 - x 3 + 3 x 4 - 2 x 5 Hence, the required answer is obtained.