Question

Find each product.$\mathbf{(}\mathbf{x}\mathbf{+}\mathbf{4}\mathbf{)}\mathbf{(}\mathbf{x}\mathbf{-}\mathbf{1}\mathbf{)}$

Short answer

The product of the given expression is $x^2+3x-4$.

Step-by-step solution

Step 1. State the concept for multiplication of algebraic expressions.

1. The product of two factors with like signs is positive, and the product of two factors with unlike signs is negative.
2. If x is a variable and m, n are positive integers, then$(x^m\times x^n)=x^{m+n}$

Step 2. State multiplication of Two Binomials.

Let $(a+b)$and $(c+d)$are two binomials. By using the distributive law of multiplication over addition twice, their product as given below.

$\begin{array}{c}(a+b)(c+d)=(a+b)\times (c+d)\\ =a\times (c+d)+b\times (c+d)\\ =(a\times c+a\times d)+(b\times c+b\times d)\\ =(ac+ad)+(bc+bd)\\ =ac+ad+bc+bd\end{array}$

Step 3. Substitute the values.

Substitute the values of a, b, c and d.

$a=x,b=4,c=x,d=-1$

$\begin{array}{c}(x+4)(x-1)=(x+4)(x+(-1))\\ =x(x+(-1))+4(x+(-1))\\ =x^2+x(-1)+4x+4(-1)\\ =x^2-x+4x-4\\ =x^2+3x-4\end{array}$

Therefore, the product of the given expression is $x^2+3x-4$.