Question

9-х2 25+х2 16х2-1 (3х+2)2 (7х-1)2

Answer 1

9-x²=(3-x)(3+x)
25-x²=(5-x)(5+x)
16x²-1=(4x-1)(4x+1)
(3x+2)²=9x²+12x+4
(7x-1)²=49x²-14x+1

Answer 2

The expression you've provided is a combination of addition, subtraction, multiplication, and exponentiation. Let's break it down step by step to simplify it.

Step 1: Rewrite the Expression

The given expression is: 9 - x^2 + 25 + x^2 + 16x^2 - 1 + (3x + 2)^2 + (7x - 1)^2

Step 2: Combine Like Terms

Combine the terms with the same variable and the constants:

9 - 1 + 25 - 1 = 32

The x^2 terms combine to give: -x^2 + x^2 + 16x^2 = 16x^2

Step 3: Expand the Squares

Expand the squares (3x + 2)^2 and (7x - 1)^2:

(3x + 2)^2 = (3x + 2)(3x + 2) = 9x^2 + 12x + 4 (7x - 1)^2 = (7x - 1)(7x - 1) = 49x^2 - 14x + 1

Step 4: Combine Like Terms

Now, combine like terms again:

32 + 16x^2 + 9x^2 + 12x + 4 + 49x^2 - 14x + 1

Combine the x^2 terms: 16x^2 + 9x^2 + 49x^2 = 74x^2

Combine the x terms: 12x - 14x = -2x

So the final simplified expression is: 74x^2 - 2x + 37

Therefore, the detailed answer to the expression 9 - x^2 + 25 + x^2 + 16x^2 - 1 + (3x + 2)^2 + (7x - 1)^2 is 74x^2 - 2x + 37.