Question

(2б+5)^2-(б-3)(3б+5)

Answer 1

(2b + 5)^2 - (b - 3)(3b + 5) = 4b^2 + 20b + 25 - (3b^2 + 2b - 15) = b^2 + 18b + 40

Answer 2

To simplify the expression $(2б+5)^2-(б-3)(3б+5)$, you'll need to expand and simplify it step by step. Here's how you can do it:

Step 1: Expand the square of the binomial $(2б+5)^2$:

$(2б+5)^2 = (2б+5)(2б+5)$

Use the FOIL (First, Outer, Inner, Last) method to expand:

$(2б+5)(2б+5) = 4б^2 + 10б + 10б + 25$

Combine like terms:

$4б^2 + 20б + 25$

Step 2: Expand the product of the two binomials $(б-3)(3б+5)$:

Use the FOIL method again:

$(б-3)(3б+5) = 3б^2 + 5б - 9б - 15$

Combine like terms:

$3б^2 - 4б - 15$

Step 3: Now, subtract the result from Step 2 from the result from Step 1:

$(4б^2 + 20б + 25) - (3б^2 - 4б - 15)$

Now, distribute the subtraction across the terms in the second expression (remember to change the signs of all terms in the second expression):

$4б^2 + 20б + 25 - 3б^2 + 4б + 15$

Combine like terms:

$(4б^2 - 3б^2) + (20б + 4б) + (25 + 15)$

Simplify further:

$б^2 + 24б + 40$

So, the simplified expression is $б^2 + 24б + 40$.