Question

Tell whether the statement about \(x^{2}+12 x+32\) is true or false. $$ x^{2}+12 x+32=(x+4)(x+8) $$

Short answer

The statement is true.

Step-by-step solution

Write down the equation

We start with the equation \(x^{2}+12 x+32 = (x+4)(x+8)\)

Expand the RHS of the equation

Now, we need to expand the RHS of the equation. A product of two binomials (in this case, (x+4)(x+8)) can be expanded by applying the distributive law (also known as FOIL method) twice. So, Eq becomes \(x^{2}+8x+4x+32\). If we further simplify it, we get \(x^{2}+12x+32\)

Compare the RHS and LHS

We compare the simplified RHS, \(x^{2}+12x+32\), with the LHS of the initial equation. Both sides are equal, which verifies the statement.