Question

Помогите с дз по алгебре. найди значение выражения (2a+1)²+2(2a+1)(a-1)+(a-1)²

Answer 1

(a+b)²=a²+2ab+b
2a+1=a      a-1=b

(2a+1)²+2(2a+1)(a-1)+(a+1)²=((2a+1)+(a-1))²=(2a+1+a-1)²=(3a)²=9a²

Answer 2

Получится вот так :)

Answer 3

Solving the Algebraic Expression

To find the value of the expression \( (2a + 1)^2 + 2(2a + 1)(a - 1) + (a - 1)^2 \), we can simplify it step by step.

First, expand the squared terms: \[ (2a + 1)^2 = (2a + 1)(2a + 1) \]

Then, apply the distributive property to the second term: \[ 2(2a + 1)(a - 1) \]

Finally, expand the squared term \( (a - 1)^2 \).

Step 1: Expand \( (2a + 1)^2 \)

\[ (2a + 1)^2 = (2a + 1)(2a + 1) = 4a^2 + 2a + 2a + 1 = 4a^2 + 4a + 1 \]

Step 2: Apply the Distributive Property to \( 2(2a + 1)(a - 1) \)

\[ 2(2a + 1)(a - 1) = 4a^2 - 2a + 2a - 1 = 4a^2 - 1 \]

Step 3: Expand \( (a - 1)^2 \)

\[ (a - 1)^2 = a^2 - 2a + 1 \]

Now, substitute the expanded forms back into the original expression: \[ (2a + 1)^2 + 2(2a + 1)(a - 1) + (a - 1)^2 = (4a^2 + 4a + 1) + (4a^2 - 1) + (a^2 - 2a + 1) \]

Simplify the expression by combining like terms: \[ 4a^2 + 4a + 1 + 4a^2 - 1 + a^2 - 2a + 1 = 9a^2 + 2a + 1 \]

So, the value of the expression \( (2a + 1)^2 + 2(2a + 1)(a - 1) + (a - 1)^2 \) is \( 9a^2 + 2a + 1 \).