(x + 1)(x + 4) =

$$x^{2}+5 x+4$$

Explanation

Multiply the first variable in the first set of parentheses with the first variable in the second set of parentheses $$\left(x \times x=x^{2}\right)$$ Next, multiply the first variable in the first set of parentheses with the second number in the second set of parentheses (x * 4 = 4x). So far, the results are $$x^{2}+4 x$$ . Now, multiply the second number in the first set of parentheses to the first vari- able in the second set of parentheses (1 * x = 1x). Next, multiply the second number in the first set of parentheses to the second number in the second set of parentheses (1 * 4 = 4). The solution is $$x^{2}+1 x+4 x+4$$ Combining the like terms results in $$x^{2}+5 x+4$$ (An easy way to remember this sequence is FOIL : First, Outside, Inside, Last.)