Question

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

Answer 1

The product of (2x + y) and (5x – y + 3) is 10x^2 + 3xy + 6x - y^2 + 3y.

Step-by-step explanation:

To find the product of (2x + y) and (5x – y + 3), we will use the distributive property of multiplication over addition. We will multiply every term of the first expression by every term of the second expression, and then combine like terms.

Starting with the first term, 2x, we multiply it by each term in the second expression:

2x * 5x = 10x^2

2x * -y = -2xy

2x * 3 = 6x

Next, we move on to the second term, y:

y * 5x = 5xy

y * -y = -y^2

y * 3 = 3y

Now, we can combine all the terms:

10x^2 - 2xy + 6x + 5xy - y^2 + 3y

Finally, combining like terms, the product of (2x + y) and (5x – y + 3) is:

10x^2 + 3xy + 6x - y^2 + 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)* (5x-y+3) = 2x* (5x-y+3) + y* (5x-y+3)` ( by applying distributive property under multiplication over addition)

⇒
`(2x+y)* (5x-y+3) = 10x^2-2xy+6x+5xy-y^2+3y` (again by distributive property)

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