What is the product of 2x + y and 5x – y + 3?
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.)
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 \(10x^2-y^2+3xy+6x+3y.\)