Factorization help

Question

Show step by step why/how the left side equals the right side.

 

Answer 1

The equation is x⁴ - 4x² + 3 = (x² - 2)² - 1.

The left hand side expression is x⁴ - 4x² + 3.

Let x² = t ⇒ t² - 4t + 3.

Write the equation in complete the square form.

x-coefficient = - 4 and add and subtract (x-coefficient/2)² = (-4/2)² = 4 to the expression.

= (t² - 4t + 3) + 4 - 4

= (t² - 4t + 4) + 3 - 4

= (t - 2)² - 1

= (x² - 2)² - 1

= right hand side expression.