Simplify the expression.
(–2y + 5)(y + 3)
The given expression is already simplified. We can only convert to standard form:
(-2y+5)(y+3) = -2y^2 - 6y +5y+15 = -2y^2 - y + 15.
To simplify the expression (–2y + 5)(y + 3), you can use the distributive property. This property states that when a number or variable is multiplied by a sum, you can distribute the multiplication to each term within the parentheses. Here's how you can simplify the expression step by step:
Step 1: Distribute –2y to each term in the second set of parentheses:
–2y(y + 3) + 5(y + 3)
Step 2: Multiply –2y by y and –2y by 3:
–2y^2 – 6y + 5(y + 3)
Step 3: Distribute 5 to each term in the second set of parentheses:
–2y^2 – 6y + 5y + 15
Step 4: Combine like terms:
–2y^2 – 6y + 5y + 15
Step 5: Combine the middle terms (-6y + 5y):
–2y^2 – y + 15
And that's the simplified expression: –2y^2 – y + 15.