Factor completely. 16-49x^(2)=

Determine the approach: Determine the approach to factor 16 - 49x^2. We can observe that both terms are perfect squares and they are subtracted from each other. This suggests that we can use the difference of squares method to factor the expression.Write in the form: Write 16 - 49x^2 in the form of a^2 - b^2. 16 can be written as 4^2 and 49x^2 can be written as (7x)^2. Therefore, we have: 16 - 49x^2 = 4^2 - (7x)^2Apply difference of squares: Apply the difference of squares formula. The difference of squares formula is a^2 - b^2 = (a - b)(a + b). We can apply this to our expression: 4^2 - (7x)^2 = (4 - 7x)(4 + 7x)Write final factored form: Write the final factored form. The factored form of 16 - 49x^2 is (4 - 7x)(4 + 7x).

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Math Problems

Algebra 1

Factor quadratics: special cases

Full solution

Q. Factor completely.

\newline

16-49x^{2}=

Determine the approach: Determine the approach to factor $16 - 49x^2$ . $\newline$ We can observe that both terms are perfect squares and they are subtracted from each other. This suggests that we can use the difference of squares method to factor the expression.
Write in the form: Write $16 - 49x^2$ in the form of $a^2 - b^2$ . $\newline$ $16$ can be written as $4^2$ and $49x^2$ can be written as $(7x)^2$ . Therefore, we have: $\newline$ $16 - 49x^2 = 4^2 - (7x)^2$
Apply difference of squares: Apply the difference of squares formula. $\newline$ The difference of squares formula is $a^2 - b^2 = (a - b)(a + b)$ . We can apply this to our expression: $\newline$ $4^2 - (7x)^2 = (4 - 7x)(4 + 7x)$
Write final factored form: Write the final factored form. $\newline$ The factored form of $16 - 49x^2$ is $(4 - 7x)(4 + 7x)$ .