The expression (4x - 1)^2 is equivalent to ax^2 + bx + c... | SAT Equivalent expressions Question, Answer Explained

Math · Advanced MathEasy

The expression $(4x - 1)^2$ is equivalent to $ax^2 + bx + c$ , where $a$ , $b$ , and $c$ are constants. What is the value of $b$ ?

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Answer: -8

Expand: $(4x - 1)^2 = (4x - 1)(4x - 1) = 16x^2 - 4x - 4x + 1 = 16x^2 - 8x + 1$ . So $b = -8$ .

Squaring each term separately gives $16x^2 + 1$ and $b = 0$ , which leaves out the middle term.

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