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Factor 16x²−9y²

a) (4x−3y)(4x+3y)
b) (4x−3y)(4x−3y)
c) (4x−3)(4x+3)
d) (x−y)(x+y)

User Dlask
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1 Answer

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Final answer:

The expression 16x²−9y² factors as (4x + 3y)(4x − 3y), because it's a difference of squares where 16x² is the square of 4x and 9y² is the square of 3y.

Step-by-step explanation:

The question is asking to factor 16x²−9y². This expression is a difference of squares, a special factoring case. Remember, the difference of squares is a binomial expression of the form a² − b² and factors into (a + b)(a − b).

To factor the given expression, identify each term as a perfect square: 16x² is the square of 4x, and 9y² is the square of 3y. Thus, the factored form of 16x²−9y² is (4x + 3y)(4x − 3y), which corresponds to choice a).

User Dsz
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