Answer :
### Detailed Step-by-Step Solution:
#### Question 1
[tex]\[ 5x - 2x - 7 \][/tex]
Combine like terms:
[tex]\[ 5x - 2x - 7 = 3x - 7 \][/tex]
To convert it to standard form [tex]\(Ax + B = 0\)[/tex]:
[tex]\[ 3x - 7 = 0 \][/tex]
#### Question 2
[tex]\[ 5 - 2x^2 = 6x \][/tex]
Move all terms to one side to set the equation to 0:
[tex]\[ -2x^2 - 6x + 5 = 0 \][/tex]
Therefore, the standard form is:
[tex]\[ -2x^2 - 6x + 5 = 0 \][/tex]
#### Question 3
[tex]\[ (x + 3)(x + 4) = 0 \][/tex]
Expand the left-hand side:
[tex]\[ x^2 + 4x + 3x + 12 = 0 \][/tex]
Combine like terms:
[tex]\[ x^2 + 7x + 12 = 0 \][/tex]
So, the standard form is:
[tex]\[ x^2 + 7x + 12 = 0 \][/tex]
#### Question 4
[tex]\[ (2x + 7)(x - 1) = 0 \][/tex]
Expand the left-hand side:
[tex]\[ 2x^2 - 2x + 7x - 7 = 0 \][/tex]
Combine like terms:
[tex]\[ 2x^2 + 5x - 7 = 0 \][/tex]
Thus, the standard form is:
[tex]\[ 2x^2 + 5x - 7 = 0 \][/tex]
#### Question 5
[tex]\[ 2x(x - 3) = 15 \][/tex]
Expand the equation and move all terms to one side:
[tex]\[ 2x^2 - 6x - 15 = 0 \][/tex]
The standard form is:
[tex]\[ 2x^2 - 6x - 15 = 0 \][/tex]
#### Question 6
[tex]\[ (x + 7)(x - 7) = -7x \][/tex]
Expand and move all terms to one side:
[tex]\[ x^2 - 49 = -7x \][/tex]
Move [tex]\(-7x\)[/tex] to the left side:
[tex]\[ x^2 + 7x - 49 = 0 \][/tex]
So, the standard form is:
[tex]\[ x^2 + 7x - 49 = 0 \][/tex]
#### Question 7
[tex]\[ (x - 4)^2 + y = 0 \][/tex]
Expand the left-hand side:
[tex]\[ x^2 - 8x + 16 + y = 0 \][/tex]
Thus, the standard form remains:
[tex]\[ x^2 - 8x + 16 + y = 0 \][/tex]
#### Question 8
[tex]\[ x + 2 = 3(x + 2) \][/tex]
Distribute and isolate the equation to make it zero:
[tex]\[ x + 2 = 3x + 6 \][/tex]
Move all terms to one side:
[tex]\[ x + 2 - 3x - 6 = 0 \][/tex]
Combine like terms:
[tex]\[ -2x - 4 = 0 \][/tex]
Thus, the standard form is:
[tex]\[ -2x - 4 = 0 \][/tex]
#### Question 9
[tex]\[ 2x - 1 = x + 1 \][/tex]
Equate the two sides and isolate the equation to make it zero:
[tex]\[ 2x - 1 - x - 1 = 0 \][/tex]
Combine like terms:
[tex]\[ x - 2 = 0 \][/tex]
So, the standard form is:
[tex]\[ x - 2 = 0 \][/tex]
#### Question 10
[tex]\[ 2(4x + 4) = x(x - 3) \][/tex]
Expand and move all terms to one side:
[tex]\[ 2(4x + 4) = x^2 - 3x \][/tex]
Distribute on the left-hand side:
[tex]\[ 8x + 8 = x^2 - 3x \][/tex]
Move all terms to one side:
[tex]\[ 8x + 8 - x^2 + 3x = 0 \][/tex]
Combine like terms:
[tex]\[ -x^2 + 11x + 8 = 0 \][/tex]
Therefore, the standard form is:
[tex]\[ -x^2 + 11x + 8 = 0 \][/tex]
### Summary
1. [tex]\( 5x - 2x - 7 \)[/tex] → [tex]\( 3x - 7 = 0 \)[/tex]
2. [tex]\( 5 - 2x^2 = 6x \)[/tex] → [tex]\( -2x^2 - 6x + 5 = 0 \)[/tex]
3. [tex]\( (x + 3)(x + 4) = 0 \)[/tex] → [tex]\( x^2 + 7x + 12 = 0 \)[/tex]
4. [tex]\( (2x + 7)(x - 1) = 0 \)[/tex] → [tex]\( 2x^2 + 5x - 7 = 0 \)[/tex]
5. [tex]\( 2x(x - 3) = 15 \)[/tex] → [tex]\( 2x^2 - 6x - 15 = 0 \)[/tex]
6. [tex]\( (x + 7)(x - 7) = -7x \)[/tex] → [tex]\( x^2 + 7x - 49 = 0 \)[/tex]
7. [tex]\( (x - 4)^2 + y = 0 \)[/tex] → [tex]\( x^2 - 8x + 16 + y = 0 \)[/tex]
8. [tex]\( x + 2 = 3(x + 2) \)[/tex] → [tex]\( -2x - 4 = 0 \)[/tex]
9. [tex]\( 2x - 1 = x + 1 \)[/tex] → [tex]\( x - 2 = 0 \)[/tex]
10. [tex]\( 2(4x + 4) = x(x - 3) \)[/tex] → [tex]\( -x^2 + 11x + 8 = 0 \)[/tex]
#### Question 1
[tex]\[ 5x - 2x - 7 \][/tex]
Combine like terms:
[tex]\[ 5x - 2x - 7 = 3x - 7 \][/tex]
To convert it to standard form [tex]\(Ax + B = 0\)[/tex]:
[tex]\[ 3x - 7 = 0 \][/tex]
#### Question 2
[tex]\[ 5 - 2x^2 = 6x \][/tex]
Move all terms to one side to set the equation to 0:
[tex]\[ -2x^2 - 6x + 5 = 0 \][/tex]
Therefore, the standard form is:
[tex]\[ -2x^2 - 6x + 5 = 0 \][/tex]
#### Question 3
[tex]\[ (x + 3)(x + 4) = 0 \][/tex]
Expand the left-hand side:
[tex]\[ x^2 + 4x + 3x + 12 = 0 \][/tex]
Combine like terms:
[tex]\[ x^2 + 7x + 12 = 0 \][/tex]
So, the standard form is:
[tex]\[ x^2 + 7x + 12 = 0 \][/tex]
#### Question 4
[tex]\[ (2x + 7)(x - 1) = 0 \][/tex]
Expand the left-hand side:
[tex]\[ 2x^2 - 2x + 7x - 7 = 0 \][/tex]
Combine like terms:
[tex]\[ 2x^2 + 5x - 7 = 0 \][/tex]
Thus, the standard form is:
[tex]\[ 2x^2 + 5x - 7 = 0 \][/tex]
#### Question 5
[tex]\[ 2x(x - 3) = 15 \][/tex]
Expand the equation and move all terms to one side:
[tex]\[ 2x^2 - 6x - 15 = 0 \][/tex]
The standard form is:
[tex]\[ 2x^2 - 6x - 15 = 0 \][/tex]
#### Question 6
[tex]\[ (x + 7)(x - 7) = -7x \][/tex]
Expand and move all terms to one side:
[tex]\[ x^2 - 49 = -7x \][/tex]
Move [tex]\(-7x\)[/tex] to the left side:
[tex]\[ x^2 + 7x - 49 = 0 \][/tex]
So, the standard form is:
[tex]\[ x^2 + 7x - 49 = 0 \][/tex]
#### Question 7
[tex]\[ (x - 4)^2 + y = 0 \][/tex]
Expand the left-hand side:
[tex]\[ x^2 - 8x + 16 + y = 0 \][/tex]
Thus, the standard form remains:
[tex]\[ x^2 - 8x + 16 + y = 0 \][/tex]
#### Question 8
[tex]\[ x + 2 = 3(x + 2) \][/tex]
Distribute and isolate the equation to make it zero:
[tex]\[ x + 2 = 3x + 6 \][/tex]
Move all terms to one side:
[tex]\[ x + 2 - 3x - 6 = 0 \][/tex]
Combine like terms:
[tex]\[ -2x - 4 = 0 \][/tex]
Thus, the standard form is:
[tex]\[ -2x - 4 = 0 \][/tex]
#### Question 9
[tex]\[ 2x - 1 = x + 1 \][/tex]
Equate the two sides and isolate the equation to make it zero:
[tex]\[ 2x - 1 - x - 1 = 0 \][/tex]
Combine like terms:
[tex]\[ x - 2 = 0 \][/tex]
So, the standard form is:
[tex]\[ x - 2 = 0 \][/tex]
#### Question 10
[tex]\[ 2(4x + 4) = x(x - 3) \][/tex]
Expand and move all terms to one side:
[tex]\[ 2(4x + 4) = x^2 - 3x \][/tex]
Distribute on the left-hand side:
[tex]\[ 8x + 8 = x^2 - 3x \][/tex]
Move all terms to one side:
[tex]\[ 8x + 8 - x^2 + 3x = 0 \][/tex]
Combine like terms:
[tex]\[ -x^2 + 11x + 8 = 0 \][/tex]
Therefore, the standard form is:
[tex]\[ -x^2 + 11x + 8 = 0 \][/tex]
### Summary
1. [tex]\( 5x - 2x - 7 \)[/tex] → [tex]\( 3x - 7 = 0 \)[/tex]
2. [tex]\( 5 - 2x^2 = 6x \)[/tex] → [tex]\( -2x^2 - 6x + 5 = 0 \)[/tex]
3. [tex]\( (x + 3)(x + 4) = 0 \)[/tex] → [tex]\( x^2 + 7x + 12 = 0 \)[/tex]
4. [tex]\( (2x + 7)(x - 1) = 0 \)[/tex] → [tex]\( 2x^2 + 5x - 7 = 0 \)[/tex]
5. [tex]\( 2x(x - 3) = 15 \)[/tex] → [tex]\( 2x^2 - 6x - 15 = 0 \)[/tex]
6. [tex]\( (x + 7)(x - 7) = -7x \)[/tex] → [tex]\( x^2 + 7x - 49 = 0 \)[/tex]
7. [tex]\( (x - 4)^2 + y = 0 \)[/tex] → [tex]\( x^2 - 8x + 16 + y = 0 \)[/tex]
8. [tex]\( x + 2 = 3(x + 2) \)[/tex] → [tex]\( -2x - 4 = 0 \)[/tex]
9. [tex]\( 2x - 1 = x + 1 \)[/tex] → [tex]\( x - 2 = 0 \)[/tex]
10. [tex]\( 2(4x + 4) = x(x - 3) \)[/tex] → [tex]\( -x^2 + 11x + 8 = 0 \)[/tex]
