1. **Problem statement:** Factorize the expressions: (c) $25x^2 - 49$ (d) $2x^2(3x - 1) - 4x$ 2. **Formula and rules:** - For (c), recognize the difference of squares formula: $$a^2 - b^2 = (a - b)(a + b)$$ - For (d), use distributive property and factor common terms. 3. **Factorizing (c):** - Identify $25x^2 = (5x)^2$ and $49 = 7^2$ - Apply difference of squares: $$25x^2 - 49 = (5x)^2 - 7^2 = (5x - 7)(5x + 7)$$ 4. **Factorizing (d):** - Expression: $$2x^2(3x - 1) - 4x$$ - Distribute $2x^2$: $$2x^2 \times 3x = 6x^3$$ $$2x^2 \times (-1) = -2x^2$$ - So expression becomes: $$6x^3 - 2x^2 - 4x$$ - Factor out the greatest common factor (GCF) $2x$: $$6x^3 - 2x^2 - 4x = 2x(3x^2 - x - 2)$$ - Now factor the quadratic inside the parentheses: Find two numbers that multiply to $3 \times (-2) = -6$ and add to $-1$. These numbers are $-3$ and $2$. Rewrite: $$3x^2 - 3x + 2x - 2$$ Group terms: $$(3x^2 - 3x) + (2x - 2)$$ Factor each group: $$3x(x - 1) + 2(x - 1)$$ Factor out common binomial: $$(3x + 2)(x - 1)$$ - So full factorization: $$2x(3x + 2)(x - 1)$$ **Final answers:** (c) $\boxed{(5x - 7)(5x + 7)}$ (d) $\boxed{2x(3x + 2)(x - 1)}$