Let's write in expanded form: ${(x-4)}^2$

ⓘ Raising a sum to an integer power is multiplying it by itself: ${(x-4)}^2$ = $(x-4)·(x-4)$

$(x-4)·(x-4)$

ⓘ Expand by multiplying each term inside the parentheses: $(x-4)·(x-4)$ = $x·x$$+x·\left(-4\right)$$-4x$$-4·\left(-4\right)$

$x·x$$+x·\left(-4\right)$$-4x$$-4·\left(-4\right)$

ⓘ Multiplying powers with the same base adds the exponents: $x·x$ = $x^2$■The minus sign is placed in front of the product: $x·\left(-4\right)$ = $-4x$■Multiplications are done before additions and subtractions. Two minus signs cancel out, the product of two negative numbers is positive: $-4·\left(-4\right)$ = $16$

$x^2$$-4x$$-4x$$+16$

ⓘ Like terms are grouped by adding their coefficients: $-4x-4x$ = $-8x$

▶Expanded form:   $x^2-8x+16$