Question

16p^4 - q^4
please answer as fast as you plz

Answer 1

Answer:

Step by Step Solution:

More Icon

STEP

1

:

Equation at the end of step 1

24p4 - q4

STEP

2

:

Trying to factor as a Difference of Squares

2.1 Factoring: 16p4-q4

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 therefore eliminated from the expression.

Check : 16 is the square of 4

Check : p4 is the square of p2

Check : q4 is the square of q2

Factorization is : (4p2 + q2) • (4p2 - q2)

Trying to factor as a Difference of Squares:

2.2 Factoring: 4p2 - q2

Check : 4 is the square of 2

Check : p2 is the square of p1

Check : q2 is the square of q1

Factorization is : (2p + q) • (2p - q)

Final result : (4p2 + q2) • (2p + q) • (2p - q)