Find the binomial that completes the factorization. t^3 + u^3 = (______)(t^2 – tu + u^2)

Apply Sum of Cubes Formula: We are given the expression t^3 + u^3 and we need to factor it into the form of (______)(t^2 – tu + u^2). To do this, we can use the sum of cubes formula, which states that a^3 + b^3 = (a + b)(a^2 - ab + b^2). Here, we can identify a with t and b with u.Factorization Using Formula: By applying the sum of cubes formula to t^3 + u^3, we get: t^3 + u^3 = (t + u)(t^2 - tu + u^2). This shows that the missing binomial in the factorization is (t + u).Check Factorization by Expansion: We can check our factorization by expanding (t + u)(t^2 - tu + u^2) to see if it equals t^3 + u^3. Expanding, we get: (t + u)(t^2 - tu + u^2) = t^3 - t^2u + tu^2 + ut^2 - u^2t + u^3 Combining like terms, we get: t^3 + u^3 This confirms that our factorization is correct.

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Algebra 2

Factor sums and differences of cubes

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Q. Find the binomial that completes the factorization.

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t^3 + u^3 = (\underline{\hspace{1cm}}) (t^2 - tu + u^2)

Apply Sum of Cubes Formula: We are given the expression $t^3 + u^3$ and we need to factor it into the form of (______)(t^2 - tu + u^2). To do this, we can use the sum of cubes formula, which states that $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$ . Here, we can identify $a$ with $t$ and $b$ with $u$ .
Factorization Using Formula: By applying the sum of cubes formula to $t^3 + u^3$ , we get: $\newline$ $t^3 + u^3 = (t + u)(t^2 - tu + u^2)$ . $\newline$ This shows that the missing binomial in the factorization is $(t + u)$ .
Check Factorization by Expansion: We can check our factorization by expanding $(t + u)(t^2 - tu + u^2)$ to see if it equals $t^3 + u^3$ . Expanding, we get: $(t + u)(t^2 - tu + u^2) = t^3 - t^2u + tu^2 + ut^2 - u^2t + u^3$ Combining like terms, we get: $t^3 + u^3$ This confirms that our factorization is correct.