Question

Determine whether the expression is a difference of squares. b^(2)+49

Answer 1

No,
`\(b^(2)+49\)` is not a difference of squares.In the case of
`\(b^(2)+49\)`, there's no subtraction between squared terms, which means it doesn't meet the criteria for a difference of squares.

Explanation:

The expression
`\(b^(2)+49\)` cannot be represented in the form of
`\(a^(2)-b^(2)\)`where
`\(a\) and \(b\)` are both squared terms. In a difference of squares, the expression would have the format
`\(a^(2)-b^(2)\)`, showcasing the subtraction of two perfect square terms.

However, in this case, the expression consists of \(b^{2}\) (a perfect square) and
`\(49\)` (also a perfect square) but without the subtraction required for a difference of squares. Thus, it doesn't conform to the specific format of a difference of squares.

A difference of squares pattern typically involves the subtraction of two squared terms, resulting in a binomial expression that factors into the product of conjugate binomials. For instance, an expression like \
`(x^(2)-9\)`fits the difference of squares pattern, as it can be factored into
`\((x+3)(x-3)\)`, showcasing the subtraction of squared terms.

In the case of
`\(b^(2)+49\)`, there's no subtraction between squared terms, which means it doesn't meet the criteria for a difference of squares.