Simplify: (s²t + tq²)² - (2stq)²

Solution:

Given, (s²t + tq²)² - (2stq)²

Using standard identity: (a + b)² = a² + 2ab + b²

Here, a = s²t and b = tq²

(s²t + tq²)² - (2stq)²

= [(s²t)² + 2(s²t)(tq²) + (tq²)²] - 4s²t²q²

= s⁴t² + 2s²t²q² + t²q⁴ - 4s²t²q²

= s⁴t² - 2s²t²q² + t²q⁴

✦ Try This: Simplify: (a⁴b - bc⁴)² + (2a²bc²)²

(a⁴b - bc⁴)² + (2a²bc²)²

Using standard identity: (a - b)² = a² - 2ab + b²

(a⁴b - bc⁴)² + (2a²bc²)²

= [(a⁴b)² - 2(a⁴b)(bc⁴) + (bc⁴)²] + 4a⁴b²c⁴

= a⁸b² - 2a⁴b²c⁴ + b²c⁸ + 4a⁴b²c⁴

= a⁸b² + 2a⁴b²c⁴ + b²c⁸

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 9

NCERT Exemplar Class 8 Maths Chapter 7 Problem 84(xiii)

Simplify: (s²t + tq²)² - (2stq)²

Summary:

Simplifying (s²t + tq²)² - (2stq)² we get, s⁴t² - 2s²t²q² + t²q⁴

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