Chapter 7: Q. 7.5 (page 643)

Simplify $\frac{2 x^{2} - 12 x y + 18 y^{2}}{3 x^{2} - 27 y^{2}}$ .

Short Answer

Expert verified

The simplest form of the given expression is $\frac{2 (x - 3 y)}{3 (x + 3 y)} .$

Step by step solution

Step 1. Given information

The given expression is $\frac{2 x^{2} - 12 x y + 18 y^{2}}{3 x^{2} - 27 y^{2}} .$

Step 2. Simplify

$\frac{2 x^{2} - 12 x y + 18 y^{2}}{3 x^{2} - 27 y^{2}} = \frac{2 (x^{2} - 6 x y + 9 y^{2})}{3 (x^{2} - 9 y^{2})} Factorthenumeratoranddenominator = \frac{2 (x - 3 y) (x - 3 y)}{3 (x - 3 y) (x + 3 y)} = \frac{2 (x - 3 y)}{3 (x + 3 y)} Removethecommonfactorsofnumeratoranddenominator$

Hence, the simplified expression is $\frac{2 (x - 3 y)}{3 (x + 3 y)} .$

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Simplify $\frac{2 x^{2} - 12 x y + 18 y^{2}}{3 x^{2} - 27 y^{2}}$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. Simplify

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Simplify2x2-12xy+18y23x2-27y2.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Simplify

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Most popular questions from this chapter

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Mechanics Maths

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Study anywhere. Anytime. Across all devices.

Simplify $\frac{2 x^{2} - 12 x y + 18 y^{2}}{3 x^{2} - 27 y^{2}}$ .