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13 November, 21:50

What is the completely factored form of 25x4-16y2

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  1. 14 November, 00:32
    0
    25x4-16y2

    Final result:

    (5x2 + 4y) • (5x2 - 4y)

    Reformatting the input:

    Changes made to your input should not affect the solution:

    (1) : "y2" was replaced by "y^2". 1 more similar replacement (s).

    Step by step solution:

    Step 1:

    Equation at the end of step 1:

    (25 • (x4)) - 24y2

    Step 2:

    Equation at the end of step 2:

    52x4 - 24y2

    Step 3:

    Trying to factor as a Difference of Squares:

    3.1 Factoring: 25x4-16y2

    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 : 25 is the square of 5

    Check : 16 is the square of 4

    Check : x4 is the square of x2

    Check : y2 is the square of y1

    Factorization is : (5x2 + 4y) • (5x2 - 4y)

    Trying to factor as a Difference of Squares:

    3.2 Factoring: 5x2 - 4y

    Check : 5 is not a square!

    Ruling : Binomial can not be factored as the

    difference of two perfect squares

    Final result:

    (5x2 + 4y) • (5x2 - 4y)

    Step-by-step explanation: i looked it up and this is what i got sorry if its wrong
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