Question

Select all the equations that are squares of linear expressions.

1) (x²)(x-2)
2) y²+10y-25
3) 49x²-196
4) (5p+2)²
5) (3x+5)²
6) (a-3)(a+3)
7) x²-14x
8) t²+16t+64
9) (2m-7)²

Answer 1

The equations that are squares of linear expressions are the second, fourth, fifth, eighth, and ninth equations from the list provided.

Step-by-step explanation:

We are asked to select all the equations that are squares of linear expressions from a given list. An equation is considered the square of a linear expression if it can be written in the form (ax + b)², where a and b are constants.

• The first equation (x²)(x-2) is not the square of a linear expression as it represents the product of x² and another linear factor.
• The second equation y²+10y-25 can be rewritten as (y+5)², which shows it is the square of a linear expression.
• The third equation 49x²-196 is not a square of a linear expression on its own.
• The fourth equation (5p+2)² is clearly the square of a linear expression.
• The fifth equation (3x+5)² is also clearly the square of a linear expression.
• The sixth equation (a-3)(a+3) represents a difference of squares, not the square of a linear expression.
• The seventh equation x²-14x is not a complete square as it lacks the constant term to complete the square.
• The eighth equation t²+16t+64 can be rewritten as (t+8)², indicating it is the square of a linear expression.
• The ninth equation (2m-7)² is the square of a linear expression as well.

Therefore, the equations that are squares of linear expressions are 2, 4, 5, 8, and 9.