Question

(2a+b)^2-(2a-3b)(2a+3b)-10b^2 И найти его значение при a=1/4, b=3

Answer 1

(2a+b)²-(2a-3b)(2a+3b)-10b²
(4a²+4ab+b²)-(4a²-9b²)-10b²
4a²+4ab+b²-4a²+9b²-10b²
4ab
4*1/4*3
1)4*1/4=4/4=1
2)1*3=3
Ответ:3

Answer 2

To find the value of the expression (2a+b)^2 - (2a-3b)(2a+3b) - 10b^2 when a = 1/4 and b = 3, we'll substitute these values into the expression and simplify.

Step 1: Substitute a and b into the expression: (2a + b)^2 - (2a - 3b)(2a + 3b) - 10b^2

Substitute a = 1/4 and b = 3:

(2 * (1/4) + 3)^2 - (2 * (1/4) - 3 * 3)(2 * (1/4) + 3 * 3) - 10 * 3^2

Step 2: Simplify each term: (2 * (1/4) + 3)^2 = (1/2 + 3)^2 = (7/2)^2 = 49/4

(2 * (1/4) - 3 * 3) = (1/2 - 9) = (-8 1/2) = -17/2

(2 * (1/4) + 3 * 3) = (1/2 + 9) = (9 1/2) = 19/2

-10 * 3^2 = -10 * 9 = -90

Step 3: Now, substitute the simplified values back into the expression:

(49/4) - (-17/2 * 19/2) - 90

Step 4: Perform the multiplication and addition:

(49/4) - (-(323/4)) - 90

Step 5: Simplify the subtraction:

(49/4) + (323/4) - 90

Step 6: Combine the fractions:

(49 + 323)/4 - 90

Step 7: Perform the addition:

(372/4) - 90

Step 8: Simplify the fraction:

93 - 90

Step 9: Perform the subtraction:

3

So, the value of the expression when a = 1/4 and b = 3 is 3.