Chapter 6: Q. 6.85 (page 612)

Factor completely: $4 x^{2} - 12 x y + 9 y^{2} - 25$

Short Answer

Expert verified

The required factors are $(2 x - 3 y - 5) (2 x - 3 y + 5)$

Step by step solution

Step 1. Given Information

The given expression is $4 x^{2} - 12 x y + 9 y^{2} - 25$

Step 2. Calculation

We will factor the expression by taking the common factor outside the paranthesis and then use the property.

$4 x^{2} - 12 x y + 9 y^{2} - 25 = {(2 x)}^{2} - 2 \times 2 x \times 3 y + {(3 y)}^{2} - 25 = {[2 x - 3 y]}^{2} - 5^{2} = (2 x - 3 y - 5) (2 x - 3 y + 5)$

Step 3. Check

We will verify by multiplying the factors.

$(2 x - 3 y - 5) (2 x - 3 y + 5) = {[2 x - 3 y]}^{2} - 5^{2} = {(2 x)}^{2} - 2 \times 2 x \times 3 y + {(3 y)}^{2} - 25 = 4 x^{2} - 12 x y + 9 y^{2} - 25$

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Factor completely: $4 x^{2} - 12 x y + 9 y^{2} - 25$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

Step 3. Check

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Factor completely:4x2-12xy+9y2-25

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

Step 3. Check

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Calculus

Probability and Statistics

Mechanics Maths

Applied Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

Factor completely: $4 x^{2} - 12 x y + 9 y^{2} - 25$