Question

Written as a simplified polynomial in standard form, what is the result when left parenthesis, x, plus, 5, right parenthesis, squared(x+5)
2
is subtracted from 7, x, squared, minus, 17x
2
−1?





Solve the problem just like the example below
⬇️
Written as a simplified polynomial in standard form, what is the result when
left parenthesis, 3, x, plus, 4, right parenthesis, squared
(3x+4)
2
is subtracted from
10
10?
Write as an expression:
Write as an expression:
10, minus, left parenthesis, 3, x, plus, 4, right parenthesis, squared
10−(3x+4)
2
10, minus, left parenthesis, 3, x, plus, 4, right parenthesis, left parenthesis, 3, x, plus, 4, right parenthesis
10−(3x+4)(3x+4)
10, minus, left parenthesis, 9, x, squared, plus, 12, x, plus, 12, x, plus, 16, right parenthesis
10−(9x
2
+12x+12x+16)
10, minus, left parenthesis, 9, x, squared, plus, 24, x, plus, 16, right parenthesis
10−(9x
2
+24x+16)
10, minus, 9, x, squared, minus, 24, x, minus, 16
10−9x
2
−24x−16
Final Answer:
Final Answer:
minus, 9, x, squared, minus, 24, x, minus, 6
−9x
2
−24x−6

Answer 1

To solve the problem, we'll follow the same structure as the example provided. The problem is to subtract \((x + 5)^2\) from \(7x^2 - 17x - 1\).

### Write as an expression:
**Write as an expression:**
\( (7x^2 - 17x - 1) - (x + 5)^2 \)

### Expand the squared term:
**Write as an expression:**
\( (7x^2 - 17x - 1) - (x + 5)(x + 5) \)
\( (7x^2 - 17x - 1) - (x^2 + 10x + 25) \)

### Distribute the negative:
**Write as an expression:**
\( 7x^2 - 17x - 1 - x^2 - 10x - 25 \)

### Combine like terms:
**Combine the like terms:**
- Combine \(7x^2 - x^2\) gives \(6x^2\)
- Combine \(-17x - 10x\) gives \(-27x\)
- Combine \(-1 - 25\) gives \(-26\)

So the expression simplifies to:
**Write as an expression:**
\( 6x^2 - 27x - 26 \)

### Final Answer:
So the final answer in standard form is:
**Final Answer:**
\(6x^2 - 27x - 26\)