Question

factorise this....
16c4-81d4​

Answer 1

Step-by-step explanation:

Changes made to your input should not affect the solution:

(1): "d4" was replaced by "d^4". 1 more similar replacement(s).

STEP

1

:

Equation at the end of step 1

(16 • (c4)) - 34d4

STEP

2

:

Equation at the end of step

2

:

24c4 - 34d4

STEP

3

:

Trying to factor as a Difference of Squares

3.1 Factoring: 16c4-81d4

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 : 81 is the square of 9

Check : c4 is the square of c2

Check : d4 is the square of d2

Factorization is : (4c2 + 9d2) • (4c2 - 9d2)

Trying to factor as a Difference of Squares:

3.2 Factoring: 4c2 - 9d2

Check : 4 is the square of 2

Check : 9 is the square of 3

Check : c2 is the square of c1

Check : d2 is the square of d1

Factorization is : (2c + 3d) • (2c - 3d)

Final result :

(4c2 + 9d2) • (2c + 3d) • (2c - 3d)

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