Chapter 6: Q. 232 (page 604)

Maribel factored $y^{2} - 30 y + 81$ as ${(y - 9)}^{2}$ . Was she right or wrong? How do you know?

Short Answer

Expert verified

The factors maribel found are wrong and the correct factors are $(y - 27) (y - 3)$

Step by step solution

Step 1. Given Information

The given expression is $y^{2} - 30 y + 81$

Step 2. Explanation

We will use perfect square trinomial pattern that is using the pattern ${(a - b)}^{2}$

The first and last terms of trinomial $y^{2} - 30 y + 81$ are perfect squares that is,

${(y)}^{2} = y^{2} = a 81 = 9^{2} = b$

Now, we will check the middle term,

$2 a b = 2 y \times 9 = 18 y$

Here middle term is not equal to the given middle term. Thus, the binomial square pattern does not fits the trinomial.

Step 3. Calculation

The given trinomial is of the form $a x^{2} + b x + c$ . By comparing it with the given expression, we get, $a = 1, b = - 30, c = 81$

Now, we will use the middle term splitting method to find the correct factors.

$y^{2} - 30 y + 81 = y^{2} - 27 y - 3 y + 81 = y (y - 27) - 3 (y - 27) = (y - 3) (y - 27)$

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Maribel factored $y^{2} - 30 y + 81$ as ${(y - 9)}^{2}$ . Was she right or wrong? How do you know?

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

Step 3. Calculation

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Maribel factored y2-30y+81as (y-9)2. Was she right or wrong? How do you know?

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

Step 3. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Decision Maths

Discrete Mathematics

Geometry

Mechanics Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Maribel factored $y^{2} - 30 y + 81$ as ${(y - 9)}^{2}$ . Was she right or wrong? How do you know?