Certainly! Let's solve the given equation step-by-step:
We are given the equation:
[tex]\[ 4. \quad x \left( 2^2 + 15 \right) + 4 \left( 2^2 + 15 \right) = (x + 4)\left(2^2 + 15\right) \][/tex]
First, simplify the expression inside the parentheses:
[tex]\[ 2^2 + 15 = 4 + 15 = 19 \][/tex]
Now, substitute 19 back into the equation:
[tex]\[ x \cdot 19 + 4 \cdot 19 = (x + 4) \cdot 19 \][/tex]
Let's distribute the multiplication on both sides:
[tex]\[ 19x + 76 = 19(x + 4) \][/tex]
Next, distribute the 19 on the right-hand side:
[tex]\[ 19x + 76 = 19x + 76 \][/tex]
This shows both sides of the equation are indeed equal.
So, the simplified form of the given expression is:
[tex]\[ 19x + 76 \][/tex]
