Answer:
[tex]\boxed {\boxed {\sf x^2+8x+16}}[/tex]
Step-by-step explanation:
To multiply two binomials (expressions with 2 terms), we can use the FOIL (first, outside, inside, last) method.
We are given this expression:
[tex](x+4)^2[/tex]
The expression (x+4) is being squared, which is equal to multiplying the term by itself twice.
[tex](x+4)(x+4)[/tex]
Next, multiply the first terms from both binomials, then repeat for the outside, inside, and last terms.
Put the products into one expression.
[tex]x^2+4x+4x+16[/tex]
Combine like terms. 4x and 4x both have the variable x, so they can be combined.
[tex]x^2+(4x+4x)+16[/tex]
[tex]x^2+8x+16[/tex]
Next, substitute 1 in for x in both the original expression and the trinomial we found. If they are equivalent, the results will be the same.
1. (x+4)²
(1+4)²
(5)² = 25 [tex]\checkmark[/tex]
2. x²+8x+16
(1)²+8(1)+16
1+8(1)+16
1+8+16
9+16= 25 [tex]\checkmark[/tex]
If x=1, both the original binomial and trinomial equal 25, so we know they are equivalent.
