Question

1)25x^4-34a^2y^2+9x^4
2)256x^4-x^2y^2+49y^4

Answer 1

Answer:

1)25x⁴-34x²y²+9x⁴

= [(5x²)² - 2×5x²×3y² +(3y²)²]- 4x²y²

=(5x² - 3y²)² - (2xy)²...by using a²-2ab + b² = (a- b)²

=( 5x² - 3y² + 2xy )( 5x² - 3y² - 2xy )...by using

(a² - b²) = (a+b)(a-b)

2) 256x⁴ - x²y² + 49y²

=[(16x²)² + 2×16x²×7y² + (7y²)²] - 225x²y²

=( 16x² + 7y²) - (15xy)²...by using a²+2ab+b²=(a+b)²

=(16x² + 7y² + 15xy)(16x² + 7y² - 15xy)...by using

a²-b² = (a+b)(a-b)

Hint: Learn how to break the term having two variables by including 2×first variable × second variable........