Question

find the product. write your answer in standard form.
$(r + 2)(r - 5)(r - 2)(r + 5)$

Explanation:

Step1: Group terms for difference of squares

Rearrange factors: $(r+2)(r-2)(r-5)(r+5)$

Step2: Apply difference of squares to pairs

First pair: $(r+2)(r-2)=r^2-2^2=r^2-4$
Second pair: $(r-5)(r+5)=r^2-5^2=r^2-25$

Step3: Multiply the two quadratic expressions

Let $A=r^2-4$ and $B=r^2-25$, compute $A\times B$:
$$(r^2-4)(r^2-25)=r^2(r^2-25)-4(r^2-25)$$

Step4: Expand and combine like terms

$$r^4-25r^2-4r^2+100=r^4-29r^2+100$$

Answer:

$\boldsymbol{r^4 - 29r^2 + 100}$