The question is
(2x+1)^2-2(2x^2-1) in simplest form
Is this correct?
[(2x+1)(2x+1)](-4x^2+2)
4x^2+2x+2x+1(-4x^2+2)
4x^2+4x+1(-4x^2+2)
-16x^4-16x^3-4x^2
+ 8x^2+8x+2
_________________________
-16^4-16x^3+4x^2+8x +2
Did I do this correctly?
Thank you for your help.
the way you typed it , I saw a subraction
(2x+1)^2 - 2(2x^2-1)
= 4x^2 + 4x + 1 - 4x^2 + 2
= 4x + 3
You did
((2x+1)^2 )(-2)(2x^2-1)
Ok, I see my mistake. Thanks for explaining what I did incorrectly.
No, your simplification is not correct.
Let's go step-by-step to simplify the given expression:
Start with the expression: (2x+1)^2 - 2(2x^2-1)
Step 1: Expand the squared term using the FOIL method:
= (2x+1)(2x+1) - 2(2x^2-1)
= (4x^2 + 2x+2x + 1) - (4x^2 - 2)
= 4x^2 + 4x + 1 - 4x^2 + 2
Step 2: Combine like terms:
= (4x^2 - 4x^2) + 4x + 2 + 1
= 4x + 3
Therefore, the simplified form of (2x+1)^2 - 2(2x^2-1) is 4x + 3.
Your final answer, -16^4-16x^3+4x^2+8x +2, does not match the simplified form.
To simplify the expression (2x+1)^2-2(2x^2-1), let's break it down step by step:
Step 1: Expand (2x+1)^2
(2x+1)^2 = (2x+1)(2x+1)
Multiply using the FOIL method:
= 2x * 2x + 2x * 1 + 1 * 2x + 1 * 1
= 4x^2 + 2x + 2x + 1
= 4x^2 + 4x + 1
Step 2: Expand -2(2x^2-1)
-2(2x^2-1) = -2 * 2x^2 + 2 * 1
= -4x^2 + 2
Step 3: Substitute the expansions into the original expression:
(2x+1)^2 - 2(2x^2-1) = (4x^2 + 4x + 1) - (-4x^2 + 2)
= 4x^2 + 4x + 1 + 4x^2 - 2
= 8x^2 + 4x - 1
Therefore, the correct simplification of the expression (2x+1)^2 - 2(2x^2-1) is 8x^2 + 4x - 1.
Your steps for simplification were incorrect, resulting in an incorrect answer. Make sure to carefully distribute the negative sign when expanding -2(2x^2 - 1). The correct answer should be 8x^2 + 4x - 1.
I hope this explanation helps! Let me know if you have any further questions.