Question

$(x - 4)(x + 4)$

1. write an equivalent expression in standard form using the box method

$(x - 10)(x + 10)$

1. which is equivalent to $(3x-8)(4x+2)$ ?

① $12x^2 + 16$
② $12x^2 - 16$
③ $12x^2 - 6x + 16$
④ $12x^2 - 26x - 16$
extra credit:
write an equivalent expression in standard form using which ever method you prefer.
$(n - 9)(n^2 + 4n - 10)$

Explanation:

Step1: Solve problem 10 (FOIL method)

Multiply using $(a-b)(a+b)=a^2-b^2$:
$(x-10)(x+10) = x^2 - 10^2 = x^2 - 100$

Step2: Solve problem 11 (FOIL method)

Multiply $(3x-8)(4x+2)$:
First: $3x \cdot 4x = 12x^2$
Outer: $3x \cdot 2 = 6x$
Inner: $-8 \cdot 4x = -32x$
Last: $-8 \cdot 2 = -16$
Combine terms: $12x^2 + 6x -32x -16 = 12x^2 -26x -16$

Step3: Solve extra credit (distribute terms)

Distribute $n$ and $-9$ to $(n^2+4n-10)$:
$n(n^2+4n-10) = n^3 +4n^2 -10n$
$-9(n^2+4n-10) = -9n^2 -36n +90$
Combine like terms:
$n^3 +4n^2 -10n -9n^2 -36n +90 = n^3 -5n^2 -46n +90$

Answer:

1. $x^2 - 100$
2. $\text{IV. } 12x^2 - 26x - 16$

Extra Credit: $n^3 - 5n^2 - 46n + 90$