We want to factor the following expression: x^(4)-14x^(2)+49 Which pattern can we use to factor the expression? U and V are either constant integers or single-variable expressions. Choose 1 answer: (A) (U+V)^(2) or (U-V)^(2) (B) (U+V)(U-V) (c) We can't use any of the patterns.

Question

We want to factor the following expression:  x^(4)-14x^(2)+49 Which pattern can we use to factor the expression?  U and  V are either constant integers or single-variable expressions. Choose 1 answer: (A)  (U+V)^(2) or  (U-V)^(2) (B)  (U+V)(U-V) (c) We can't use any of the patterns.

Bytelearn · Accepted Answer

Rephrasing the problem: First, let's rephrase the  ＂What pattern can be used to factor the expression x^4 - 14x^2 + 49?＂Identifying the structure: Identify the structure of the given expression: x^4 - 14x^2 + 49. Notice that it resembles the structure of a perfect square trinomial, which is a^2 - 2ab + b^2 or a^2 + 2ab + b^2, where the first and last terms are perfect squares and the middle term is twice the product of the square roots of the first and last terms.Checking for perfect squares: Determine if the first term (x^4) and the last term (49) are perfect squares. The first term x^4 is a perfect square because (x^2)^2 = x^4. The last term 49 is a perfect square because 7^2 = 49.Verifying the middle term: Check if the middle term (-14x^2) fits the pattern of twice the product of the square roots of the first and last terms. The square root of x^4 is x^2, and the square root of 49 is 7, so twice the product of x^2 and 7 is 2 * x^2 * 7 = 14x^2. Since the middle term is -14x^2, it fits the pattern of a perfect square trinomial with a negative middle term, which corresponds to (a - b)^2.Writing as a perfect square trinomial: Write the expression as a perfect square trinomial using the pattern (a - b)^2, where a is the square root of the first term and b is the square root of the last term. In this case, a = x^2 and b = 7, so the factored form is (x^2 - 7)^2.

Full solution

More problems from Mean, median, mode, and range: find the missing number

Related topics