1. **State the problem:** Factor each of the given expressions: - $64b^4 - 81$ - $4x^2 - 25x$ - $9x^2 - 30x + 25$ - $25x^2 - 144y^2$ 2. **Recall formulas and rules:** - Difference of squares: $$a^2 - b^2 = (a - b)(a + b)$$ - Factoring out common factors - Perfect square trinomials: $$a^2 - 2ab + b^2 = (a - b)^2$$ - Difference of squares applies to expressions like $25x^2 - 144y^2$ 3. **Factor each expression:** **(a) $64b^4 - 81$** - Recognize as difference of squares: $64b^4 = (8b^2)^2$, $81 = 9^2$ - Apply formula: $$64b^4 - 81 = (8b^2 - 9)(8b^2 + 9)$$ **(b) $4x^2 - 25x$** - Factor out common factor $x$: $$4x^2 - 25x = x(4x - 25)$$ **(c) $9x^2 - 30x + 25$** - Recognize as perfect square trinomial: $$9x^2 = (3x)^2, \, 25 = 5^2, \, -30x = -2 \times 3x \times 5$$ - Factor as: $$(3x - 5)^2$$ **(d) $25x^2 - 144y^2$** - Recognize as difference of squares: $$25x^2 = (5x)^2, \, 144y^2 = (12y)^2$$ - Apply formula: $$(5x - 12y)(5x + 12y)$$ 4. **Final factored forms:** - $64b^4 - 81 = (8b^2 - 9)(8b^2 + 9)$ - $4x^2 - 25x = x(4x - 25)$ - $9x^2 - 30x + 25 = (3x - 5)^2$ - $25x^2 - 144y^2 = (5x - 12y)(5x + 12y)$