Mastering The Foil Method: How To Multiply (X + 3)(X^2 – 2X + 5)

Perform the operations.(x + 3)(x^2 – 2x + 5)

x^3 + x^2 – x + 15

To perform the given operations of (x + 3)(x^2 – 2x + 5), we can use the distributive property of multiplication. This means that we need to multiply each term in the first set of parentheses by each term in the second set of parentheses and then combine like terms. We can use the FOIL method to help with this process.

FOIL stands for:

First terms: Multiply the first term in each set of parentheses.

Outer terms: Multiply the outer term in each set of parentheses.

Inner terms: Multiply the inner term in each set of parentheses.

Last terms: Multiply the last term in each set of parentheses.

So, using the FOIL method, we get:

(x + 3)(x^2 – 2x + 5) = x(x^2) + x(-2x) + x(5) + 3(x^2) + 3(-2x) + 3(5)

Simplifying each term, we get:

(x + 3)(x^2 – 2x + 5) = x^3 – 2x^2 + 5x + 3x^2 – 6x + 15

Combining like terms, we finally get:

(x + 3)(x^2 – 2x + 5) = x^3 + x^2 – x + 15

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