Question

Show that :- (3x+7)² - 84 x = ( 3x – 7)²​

Answer 1

To Prove :-

(3x + 7)² – 84 x = (3x – 7)²

Proof :-

➨ (3x + 7)² – 84x = (3x – 7)²

Use Identities :-

• (a + b)² = a² + b² + 2ab.

• (a – b)² = a² + b² – 2ab.

➨ (3x)² + 7² + (2)(3x)(7) – 84x = (3x)² + 7² – (2)(3x)(7).

➨ 9x² + 49 + 42x – 84x = 9x² + 49 – 42x.

➨ 9x² + 49 – 42x = 9x² + 49 – 42x.

Use Transposition.

➨ 9x² – 9x² – 42x + 42x = 49 – 49.

➨ 0 = 0.

LHS = RHS.

Hence, Verified.

Some Identities to Remember :-

• (a + b)² = a² + b² + 2ab.

• (a – b)² = a² + b² – 2ab.

• (a)² – (b)² = (a + b)(a – b).

Answer 2

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