Questions: Multiply the binomials using the FOIL method. Combine like terms. [ (x^3+4)(6 x^3+6) ]

Transcript text: Multiply the binomials using the FOIL method. Combine like terms. \[ \left(x^{3}+4\right)\left(6 x^{3}+6\right) \]

Solution

Step 1: First (F)

First terms multiplied: \(a \cdot c \cdot x^{m+n}\) = 6x^6

Step 2: Outer (O)

Outer terms multiplied: \(a \cdot d \cdot x^m\) = 30x^3

Step 3: Inner (I)

Inner terms multiplied: \(b \cdot c \cdot x^n\) = 30x^3

Step 4: Last (L)

Last terms multiplied: \(b \cdot d\) = 24

Combining Like Terms

Combining like terms gives: 6x^6 + 30x^3 + 24

The product of the binomials is 6x^6 + 30x^3 + 24

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