Question

Factorize 64 x¹³y + 343 xy¹³

Answer 1

Answer:

xy (4x⁴+ 7y⁴) (16x⁸ + 49y⁸ -28x⁴y⁴)

Step-by-step explanation:

To find --->

Factors of 64x¹³ y + 343 x y¹³

Solution--->

64 x¹³ y + 343 x y¹³

= x y ( 64 x¹² + 343 y¹² )

= x y { ( 4 x⁴ )³ + ( 7 y⁴ )³ }

We have an identity

(a³+ b³) = (a + b ) (a² + b² - ab )

Applying it here we get

= xy ( 4 x⁴ + 7 y⁴) {(4x⁴)² + (7y⁴)² -

(4x⁴)(7y⁴)}

=xy (4x⁴ +7y⁴) (16x⁸ + 49y⁸ - 28x⁴y⁴ )

Additional information--->

1) a³ - b³ = (a - b ) (a² + b² + ab )

2) a² - b² = (a + b ) ( a - b )

3) (a + b )² = a² + b² + 2 ab

4) (a - b )² = a² + b² - 2ab

5) (a + b + c )²= a²+ b²+ c²+2ab+2ac+2bc

6) (a + b)³ = a³ + b³ + 3ab(a + b )

7) (a - b )³= a³ - b³ - 3ab ( a - b )