Question

review
simplify the following expressions.

1. (x+1)(x-1) 2) (x-5)(x+5) 3) (3-p)(3+p)

difference of perfect squares (dops)
factor the following expressions.

1. x² - 9 5) x² - 25 6) x² - 16

1. 1 - y² 8) m² - 100 9) h² - k²

Explanation:

Step1: Apply difference of squares rule

For $(a+b)(a-b)=a^2-b^2$

1. $(x+1)(x-1)=x^2-1^2=x^2-1$
2. $(x-5)(x+5)=x^2-5^2=x^2-25$
3. $(3-p)(3+p)=3^2-p^2=9-p^2$

Step2: Factor via difference of squares

For $a^2-b^2=(a+b)(a-b)$

1. $x^2-9=x^2-3^2=(x+3)(x-3)$
2. $x^2-25=x^2-5^2=(x+5)(x-5)$
3. $x^2-16=x^2-4^2=(x+4)(x-4)$
4. $1-y^2=1^2-y^2=(1+y)(1-y)$
5. $m^2-100=m^2-10^2=(m+10)(m-10)$
6. $h^2-k^2=(h+k)(h-k)$

Answer:

1. $x^2 - 1$
2. $x^2 - 25$
3. $9 - p^2$
4. $(x+3)(x-3)$
5. $(x+5)(x-5)$
6. $(x+4)(x-4)$
7. $(1+y)(1-y)$
8. $(m+10)(m-10)$
9. $(h+k)(h-k)$