Question

factorize completely- p^x-4q^x

Answer 1

Answer:

((p^2) • x) - (2^2q^2 • x)

3.1 Pull out like factors :

p^2x - 4xq^2 = x • (p^2 - 4q^2)

3.2 Factoring: p^2 - 4q^2

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 : 4 is the square of 2

Check : p^2 is the square of p1

Check : q^2 is the square of q1

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

Final result :

x • (p + 2q) • (p - 2q)

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