### Home > AC > Chapter 14 > Lesson 14.3.1.5 > Problem3-69

3-69.

Determine which of the following equations are true for all values (always true). For those that are not, decide whether they are true for certain values (sometimes true) or not true for any values (never true). Justify your decisions clearly.

1.  $(x-5)^2=x^2+25$

Solve the equation. Remember, $(x − 5)^2 = (x − 5)(x − 5)$.

If the equation has a solution, it is sometimes true.
If the equation has no solution, it is never true.
If the equation is an identity (true no matter which values are chosen for variables), it is always true.

Sometimes true (when $x = 0$).

1.  $(2x-1)(x+4)=2x^2+7x-4$

Refer to part (a).

Always true.

1.  $\frac{2x^2y^3}{y^2}=2x^2y$

1.  $(3x-2)(2x+1)=6x^2-x-5$