Question

Solve the following

625x⁴ - 81y²
​

Answer 1

Answer:

(25x2 + 9y) • (25x2 - 9y)

Step-by-step explanation:

(625 • (x4)) - 34y2

54x4 - 34y2

Factoring: 625x4-81y2

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefo eliminated from the expression.

Check : 625 is the square of 25

Check : 81 is the square of 9

Check : x4 is the square of x2

Check : y2 is the square of y1

Factorization is : (25x2 + 9y) • (25x2 - 9y)

Factoring: 25x2 - 9y

Check : 25 is the square of 5

Check : 9 is the square of 3

Check : x2 is the square of x1

Answer 2

Answer:

the question 625x⁴ - 81y² is not possible because the are unlike terms and subtraction of unlike term is not possible.