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What explains why y = 4x² + 49 is not valid for factoring with difference of squares.

(A) The equation is not a binomial
(B) The equation is not a difference
(C) The terms are not squares
(D) y = (2x - 7)(2x - 7)
(E) y = (2x + 7)(2x + 7)

User Andrewsh
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1 Answer

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Final answer:

The equation y = 4x² + 49 cannot be factored using the difference of squares because the equation is a sum, not a difference, although the individual terms are indeed perfect squares.

Step-by-step explanation:

The expression y = 4x² + 49 is not valid for factoring with difference of squares because option (B) The equation is not a difference is the correct answer. A difference of squares occurs when an expression can be written as a² - b², which is not the case here since we have a sum 4x² + 49, not a difference. Furthermore, (C) The terms are not squares is incorrect since both 4x² ((2x)²) and 49 (7²) are indeed perfect squares. Options (D) and (E) are expansions of binomials, not factorizations in the context of a difference of squares.

User Dieter Meemken
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