What is that product of 2x + y and 5x - y + 3?

Solution:

The problem statement above can be formulated as multiplication of algebraic expressions.

(2x + y)(5x - y + 3)

The above can be expanded as:

(2x + y)(5x) - y(2x+y) + 3(2x + y)

= (2x)(5x) +(y)(5x) -(y)(2x) -y(y) + (3)(2x) + 3(y) (applying the distributive property)

= 10x² + 5xy - 2xy - y² + 6x + 3y(grouping the like terms)

(2x + y)(5x - y + 3) = 10x² + 6x + 3xy + 3y - y²

What is that product of 2x + y and 5x - y + 3?

Summary:

The above problem is an illustration of the simple multiplication of two algebraic expressions comprising variables x and y. The resultant equation which is the solution i.e. 10x² + 6x + 3xy + 3y - y² is a polynomial with the degree of the equation being 2.