Question

factorize (x²-5x+6)(x²+5x+6) -2x²
plz need urgent
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Answer 1

Given

factorize (x²-5x+6)(x²+5x+6) -2x²

Solution

Applying identity → a² - b² = (a+b)(a-b)

= (x²-5x+6)(x²+5x+6) -2x²

= [(x² - 5x)² - (6)²] - 2x²

Again, applying identity

(a-b)²= a² + b²- 2ab

= [{(x²)² + (5x)² - 2*x²*5x} - 36] -2x²

= [x⁴ + 25x² - 10x³ - 36] - 2x²

= x⁴ - 10x³ + 25x² - 2x² - 36

= x⁴ - 10x³ + 23x² - 36

Some important identities

• (a+b)² = a² + b² +2ab
• (a-b)² = a² + b² - 2ab
• (a+b)³ = a³ + b³ + 3ab(a+b)
• (a-b)³ = a³ -b³ - 3ab(a-b)
• a² - b² = (a+b)(a-b)
• a³ + b³ = (a+b)(a² - ab +b²)
• a³ - b³ = (a-b)(a² + ab +b²)