**(i) 20x ^{2} – 45y^{2}**

**(ii) 9x ^{2} – 4(y + 2x)^{2}**

**Answer :**

**(i) 20x**^{2} – 45y^{2}

^{2}– 45y

^{2}

Take out common in all terms,

5(4x^{2} – 9y^{2})

5((2x)^{2} – (3y)^{2})

We know that, a^{2} – b^{2} = (a + b) (a – b)

5(2x + 3y) (2x – 3y)

**(ii) 9x**^{2} – 4(y + 2x)^{2}

^{2}– 4(y + 2x)

^{2}

9x^{2} – 4(y + 2x)^{2}

Above question can be written as,

(3x)^{2} – [2(y + 2x)]^{2}

(3x)^{2} – (2y + 4x)^{2}

We know that, a^{2} – b^{2} = (a + b) (a – b)

(3x + 2y + 4x) (3x – 2y – 4x)

(7x + 2y) (-x – 2y)

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