1Cademy - Simplifying $$(3 - 2\sqrt{7})(4 - 2\sqrt{7})$$ and $$(\sqrt[3]{x}

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The FOIL Method for Multiplying Binomials

Example

Simplifying $(3 - 2\sqrt{7})(4 - 2\sqrt{7})$ and $(\sqrt[3]{x} - 2)(\sqrt[3]{x} + 4)$

To multiply binomials that contain radical expressions, such as $(3 - 2\sqrt{7})(4 - 2\sqrt{7})$ and $(\sqrt[3]{x} - 2)(\sqrt[3]{x} + 4)$ , use the FOIL method to organize the four products before combining like terms. For the first product, applying FOIL yields $12 - 6\sqrt{7} - 8\sqrt{7} + 4(7)$ . Simplifying the constants and combining the like radicals gives $12 - 14\sqrt{7} + 28$ , which simplifies to $40 - 14\sqrt{7}$ . For the second product, multiplying the binomials yields $\sqrt[3]{x^2} + 4\sqrt[3]{x} - 2\sqrt[3]{x} - 8$ . Combining the like terms in the middle gives the simplified expression $\sqrt[3]{x^2} + 2\sqrt[3]{x} - 8$ .

Updated 2026-05-01

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OpenStax Intermediate Algebra

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