Chapter ISG, Problem 8.7.2.1P

To determine

To verify a statement and correct if incorrect.

Answer to Problem 8.7.2.1P

Statement is incorrect. Correct expression: $9x^2+30x+25$

Explanation of Solution

Given information:

Expression: $9x^2+50x+25$

Calculation:

To verify the statement,

A perfect square trinomial is said to be an expression having

• 3 terms
• two of its terms should be perfect square itself
• The remaining term is twice the product of square roots of other two terms,

Now, the expression $9x^2+50x+25=0$ is not a perfect term because the coefficient of x is not the twice of sum of square roots of other two terms.

To make the expression correct, use identity ${(a+b)}^2=a^2+2ab+b^2$

Comparing the terms,

  $a=3x,b=5$

For $2ab$ , expand 50x ,

  $50x=$

  $2\times 5\times 5\times x$

To make the expression correct, divide by 5 and multiply by 3 for correct term,

  = $\frac{2(5)(5)(x)}{5}\times 3$

Solving,

  = $30x$ .

Now the expression corrected is: $9x^2+30x+25$