Question

what is the common factors of 4p, -16pq^2, 20p^2 q​​

Answer 1

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

(20 • (p2)) - (24p2 • q2)

STEP

2

:

Equation at the end of step

2

:

(22•5p2) - 24p2q2

STEP

3

:

STEP

4

:

Pulling out like terms

4.1 Pull out like factors :

20p2 - 16p2q2 = -4p2 • (4q2 - 5)

Trying to factor as a Difference of Squares:

4.2 Factoring: 4q2 - 5

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 : 5 is not a square !!

Ruling : Binomial can not be factored as the difference of two perfect squares.

Final result :

-4p2 • (4q2 - 5)

Answer 2

Answer:

4p

Step-by-step explanation:

$\huge \red{factors}$

4p , -16pq² , 20 p²

Here , we can see that , 4p is repeating in each terms . so 4p is the common factor.

i.e. 4p ( 1 , - 4q² , 5p)