Question
Factor.
64 x squared plus 16 x plus 1
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Part 1
64 x squared plus 16 x plus 1equals
enter your response here (Factor completely.)
64 x squared plus 16 x plus 1
Question content area bottom
Part 1
64 x squared plus 16 x plus 1equals
enter your response here (Factor completely.)
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To factor the expression \( 64x^2 + 16x + 1 \), we can use the method of factoring a perfect square trinomial.
First, we can check if the expression is a perfect square trinomial. A perfect square trinomial can be expressed in the form \( (ax + b)^2 \).
1. Identify the first term: \( 64x^2 \) can be written as \( (8x)^2 \).
2. Identify the last term: \( 1 \) can be written as \( (1)^2 \).
3. The middle term \( 16x \) can be expressed as \( 2 \times (8x) \times (1) \), which matches the form of a perfect square.
Thus, \( 64x^2 + 16x + 1 \) can be factored as:
\[
(8x + 1)^2
\]
So,
\[
64x^2 + 16x + 1 = (8x + 1)(8x + 1) = (8x + 1)^2.
\]
Final answer:
\[
64x^2 + 16x + 1 = (8x + 1)^2.
\]
First, we can check if the expression is a perfect square trinomial. A perfect square trinomial can be expressed in the form \( (ax + b)^2 \).
1. Identify the first term: \( 64x^2 \) can be written as \( (8x)^2 \).
2. Identify the last term: \( 1 \) can be written as \( (1)^2 \).
3. The middle term \( 16x \) can be expressed as \( 2 \times (8x) \times (1) \), which matches the form of a perfect square.
Thus, \( 64x^2 + 16x + 1 \) can be factored as:
\[
(8x + 1)^2
\]
So,
\[
64x^2 + 16x + 1 = (8x + 1)(8x + 1) = (8x + 1)^2.
\]
Final answer:
\[
64x^2 + 16x + 1 = (8x + 1)^2.
\]
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