Question

(x² + 8)(x² - 2) with a box - method (area model) showing top row terms ( x^2 ), ( +8 ) and left - column terms ( x^2 ), ( -2 ); box cells contain terms like ( +4 ) (possibly ( x^4 ) with a typo), ( 8x^2 ), ( -16 ), and a partially visible term in the bottom - left cell

Explanation:

Step1: Identify the terms to multiply

We have the two binomials $(x^2 + 8)$ and $(x^2 - 2)$. We will use the distributive property (FOIL method or box method as shown).

Step2: Multiply the first terms

Multiply $x^2$ (from the first binomial) and $x^2$ (from the second binomial): $x^2 \times x^2 = x^4$.

Step3: Multiply the outer terms

Multiply $x^2$ (from the first binomial) and $-2$ (from the second binomial): $x^2 \times (-2) = -2x^2$.

Step4: Multiply the inner terms

Multiply $8$ (from the first binomial) and $x^2$ (from the second binomial): $8 \times x^2 = 8x^2$.

Step5: Multiply the last terms

Multiply $8$ (from the first binomial) and $-2$ (from the second binomial): $8 \times (-2) = -16$.

Step6: Combine like terms

Now, combine the middle terms ($-2x^2$ and $8x^2$): $-2x^2 + 8x^2 = 6x^2$.

Step7: Write the final polynomial

Putting it all together, we have $x^4 + 6x^2 - 16$.

Answer:

$x^4 + 6x^2 - 16$