1. **State the problem:** Factor each algebraic expression. 2. **Expression 1: $64 b^4 - 81$** - Recognize this as a difference of squares: $a^2 - b^2 = (a-b)(a+b)$. - Here, $64 b^4 = (8 b^2)^2$ and $81 = 9^2$. - So, $$64 b^4 - 81 = (8 b^2)^2 - 9^2 = (8 b^2 - 9)(8 b^2 + 9).$$ - Note that $8 b^2 - 9$ is not a difference of squares since 9 is a perfect square but 8 is not. 3. **Expression 2: $4x^2 - 25x$** - Factor out the greatest common factor (GCF): $x$. - $$4x^2 - 25x = x(4x - 25).$$ 4. **Expression 3: $9x^2 - 30x + 25$** - Recognize this as a perfect square trinomial: $a^2 - 2ab + b^2 = (a - b)^2$. - Here, $9x^2 = (3x)^2$, $25 = 5^2$, and $-30x = -2 imes 3x imes 5$. - So, $$9x^2 - 30x + 25 = (3x - 5)^2.$$ 5. **Expression 4: $25x^2 - 144y^2$** - Recognize this as a difference of squares: $a^2 - b^2 = (a-b)(a+b)$. - Here, $25x^2 = (5x)^2$ and $144y^2 = (12y)^2$. - So, $$25x^2 - 144y^2 = (5x - 12y)(5x + 12y).$$