Question

factorization: (4x^2 - 1)(4y^2 - 1) + 16xy​

Answer 1

Answer:

45

Step-by-step explanation:

hope it help

Answer 2

Step by step solution :

Step 1 :

Equation at the end of step 1 :

((1-(4•(x2)))•(1-22y2))+16xy

Step 2 :

Equation at the end of step 2 :

((1 - 22x2) • (1 - 4y2)) + 16xy

Step 3 :

Trying to factor as a Difference of Squares :

3.1 Factoring: 1-4x2Theory : 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 : 1 is the square of 1

Check : 4 is the square of 2

Check : x2 is the square of x1

Factorization is : (1 + 2x) • (1 - 2x)

Trying to factor as a Difference of Squares :

3.2 Factoring: 1 - 4y2

Check : 1 is the square of 1

Check : 4 is the square of 2

Check : y2 is the square of y1

Factorization is : (1 + 2y) • (1 - 2y)

Equation at the end of step 3 :

(2x+1)•(1-2x)•(2y+1)•(1-2y)+16xy

Step 4 :

Final result :

16x2y2 - 4x2 + 16xy - 4y2 + 1

hope it help you