Question

What is the product of 2x + y and 5x – y + 3?

Answer 1

Answer:  The required product is $10x^2-y^2+3xy+6x+3y.$

Step-by-step explanation:  We are to find the product f the following two algebraic expressions:

$E_1=2x+y,\\\\E_2=5x-y+3.$

To find the product of the above two expressions, we must multiply each term of the first expression with each term of the second expression.

The multiplication is as follows:

$M\\\\=E_1 \times E_2\\\\=(2x+y)\times(5x-y+3)\\\\=10x^2-2xy+6x+5xy-y^2+3y\\\\=10x^2-y^2+3xy+6x+3y.$

Thus, the required product is $10x^2-y^2+3xy+6x+3y.$

Answer 2

Answer: $10x^2-y^2+3xy+6x+3y$

Step-by-step explanation:

Given expressions are 2x+ y and 5x -y +3

Product of 2x+y and 5x-y+3 is

$(2x+y)\times (5x-y+3) = 2x\times (5x-y+3) + y\times (5x-y+3)$ ( by applying distributive property under multiplication over addition)

⇒$(2x+y)\times (5x-y+3) = 10x^2-2xy+6x+5xy-y^2+3y$ (again by distributive property)

⇒$(2x+y)\times (5x-y+3) = 10x^2-y^2+3xy+6x+3y$  ( by operating the like terms.)