Expand and simplify.
12-2(3y-2)(3y+2)-(2y+5)(2y+5)
Textbook Answer: -22y^2-20y-5
I don't know how to get that. Can someone show me the step by step process?
thank you very much.
12-2(9y^2-4)-(4y^2+20y+25)
12-18y^2+8-4y^2-20y-25
combine like terms
-22y^2-20Y-5
To expand and simplify the given expression, let's break it down into smaller steps:
Step 1: Apply the distributive property
12 - 2(3y - 2)(3y + 2) - (2y + 5)(2y + 5)
= 12 - 2(9y^2 - 4) - (4y^2 + 20y + 25)
Step 2: Simplify the inner parentheses
= 12 - 18y^2 + 8 - 4y^2 - 20y - 25
Step 3: Combine like terms
= -22y^2 - 20y - 5
Therefore, the simplified expression is -22y^2 - 20y - 5.
Keep in mind that when applying the distributive property, you need to distribute the outer expression (in this case, -2 and -1) to every term inside the parentheses. Also, make sure to simplify each pair of parentheses first before combining like terms.