Expand and simplify (7x + 7)(x^2 + 4x - 7).

Step-by-step solution

1. 1

   Plan the distribution. Each of the $2$ terms in the first bracket multiplies each of the $3$ terms in the second, giving $6$ products before any collecting. FOIL does not apply here — it is only a mnemonic for two binomials.

2. 2

   Distribute the first term, 7x.

   $7x\left(x^2 + 4x - 7\right) = 7x^3 + 28x^2 - 49x$

3. 3

   Distribute the second term, 7.

   $7\left(x^2 + 4x - 7\right) = 7x^2 + 28x - 49$

4. 4

   Add the two results and collect like terms.

   $7x^3 + \left(28x^2 + 7x^2\right) + \left(-49x + 28x\right) - 49 = 7x^3 + 35x^2 - 21x - 49$

5. 5

   Check the factored structure. Since $7x + 7 = 7(x+1)$, the answer must be divisible by $7$ — and indeed every coefficient $7, 35, -21, -49$ is a multiple of $7$, giving $7\left(x^3 + 5x^2 - 3x - 7\right)$. That is a quick structural check that no term was dropped.

6. 6

   Verify numerically at x = 2. The original is $(14 + 7)(4 + 8 - 7) = 21 \times 5 = 105$. The expansion gives $56 + 140 - 42 - 49 = 105$. They match.