Question

find the square of (n+12)^2

Answer 1

(n+12)^(2)

Squaring an expression is the same as multiplying the expression by itself 2 times.
(n+12)(n+12)

Multiply each term in the first group by each term in the second group using the FOIL method. FOIL stands for First Outer Inner Last, and is a method of multiplying two binomials. First, multiply the first two terms in each binomial group. Next, multiply the outer terms in each group, followed by the inner terms. Finally, multiply the last two terms in each group.
(n*n+n*12+12*n+12*12)

Multiply n by n to get n^(2).
(n^(2)+n*12+12*n+12*12)

Multiply n by 12 to get 12n.
(n^(2)+12n+12*n+12*12)

Multiply 12 by n to get 12n.
(n^(2)+12n+12n+12*12)

Multiply 12 by 12 to get 144.
(n^(2)+12n+12n+144)

According to the distributive property, for any numbers a, b, and c, a(b+c)=ab+ac and (b+c)a=ba+ca. Here, n is a factor of both 12n and 12n.
(n^(2)+(12+12)n+144)

Add 12 to 12 to get 24.
(n^(2)+(24)n+144)

Remove the parentheses.
(n^(2)+24n+144)

Remove the parentheses around the expression n^(2)+24n+144.
n^(2)+24n+144