Question

factorise using an identity:4a^2-16b^8​

Answer 1

Answer:

STEP

1

:

Equation at the end of step 1

(4 • (a2)) - 24b2

STEP

2

:

Equation at the end of step

2

:

22a2 - 24b2

STEP

3

:

STEP

4

:

Pulling out like terms

4.1 Pull out like factors :

4a2 - 16b2 = 4 • (a2 - 4b2)

Trying to factor as a Difference of Squares:

4.2 Factoring: a2 - 4b2

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 : a2 is the square of a1

Check : b2 is the square of b1

Factorization is : (a + 2b) • (a - 2b)

Final result :

4 • (a + 2b) • (a - 2b)

Answer 2

4a² - 16$b^{8}$ = (2a)² - (4$b^{4}$)²

Now you can use identity (a²- b²) = (a+b) (a-b)

so the answer is (2a + 4$b^{4}$) (2a - 4$b^{4}$)

Hope it helps you..