Question

Г) (4х-5)(4х+5)+18^2= д) 3 (х-2)^2-(2х+5)(2х-5)=​

Answer 1

Г)16х²+299

Д)-х²-12х +37

Answer 2

To simplify the given expressions, let's solve them step by step:

a) (4x-5)(4x+5)+18^2:

First, we can use the formula for the difference of squares, which states that (a^2 - b^2) can be factored as (a+b)(a-b). In this case, we have (4x-5)(4x+5), which can be written as (4x)^2 - (5)^2.

Using the difference of squares formula, we have: (4x-5)(4x+5) = (4x)^2 - (5)^2

Simplifying further: (16x^2 - 25) + 18^2

Calculating 18^2: (16x^2 - 25) + 324

Combining like terms: 16x^2 - 25 + 324

Simplifying: 16x^2 + 299

So, the simplified expression is 16x^2 + 299.

b) 3(x-2)^2 - (2x+5)(2x-5):

Let's simplify this expression step by step.

First, let's expand (x-2)^2: (x-2)^2 = (x-2)(x-2) = x^2 - 2x - 2x + 4 = x^2 - 4x + 4

Now let's expand (2x+5)(2x-5): (2x+5)(2x-5) = (2x)^2 - (5)^2 = 4x^2 - 25

Now we can substitute the expanded forms back into the expression: 3(x-2)^2 - (2x+5)(2x-5) = 3(x^2 - 4x + 4) - (4x^2 - 25)

Expanding further: 3x^2 - 12x + 12 - 4x^2 + 25

Combining like terms: -x^2 - 12x + 37

So, the simplified expression is -x^2 - 12x + 37.