The polynomial \( 16x^8 - 49x^2 \) can be recognized as a difference of squares, where it can be rewritten as \( (4x^4)^2 - (7)^2 \).
This matches the pattern \( a^2 - b^2 = (a - b)(a + b) \).
Thus, the correct answer is:
A. (a−b)(a+b)=a^2−b^2
Which pattern can be used to factor the high-degree polynomial 16x^8−49x^2?(1 point)
A. (a−b)(a+b)=a2−b2
B. (a−b)2=a2−2ab+b2
C. Neither the difference of squares nor the perfect square trinomial pattern can be used to factor 16x8−49x2.
D. (a+b)^2=a^2+2ab+b^2
3 answers
Are you sure
Yes, I am sure. Let's break it down again to clarify:
The expression \( 16x^8 - 49x^2 \) can be factored by first recognizing it as a difference of squares:
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Identify \( a \) and \( b \):
- \( a^2 = 16x^8 \) which implies \( a = 4x^4 \)
- \( b^2 = 49 \) which implies \( b = 7 \)
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Use the difference of squares formula: The formula for the difference of squares is: \[ a^2 - b^2 = (a - b)(a + b) \] Plugging in our values we have: \[ 16x^8 - 49 = (4x^4 - 7)(4x^4 + 7) \]
Therefore, the polynomial \( 16x^8 - 49x^2 \) can be factored using the difference of squares pattern.
So, option A is indeed the right choice.
1 answer