1. **State the problem:** Factorise the expression $$(5x - 3)(14x - 4) - (7x - 2)^2$$. 2. **Recall the formulas:** - Use distributive property (FOIL) to expand products. - Use the formula for square of a binomial: $$(a - b)^2 = a^2 - 2ab + b^2$$. 3. **Expand each term:** - Expand $$(5x - 3)(14x - 4)$$: $$5x \times 14x = 70x^2$$ $$5x \times (-4) = -20x$$ $$-3 \times 14x = -42x$$ $$-3 \times (-4) = 12$$ So, $$(5x - 3)(14x - 4) = 70x^2 - 20x - 42x + 12 = 70x^2 - 62x + 12$$. - Expand $$(7x - 2)^2$$ using the formula: $$a = 7x, b = 2$$ $$ (7x)^2 - 2 \times 7x \times 2 + 2^2 = 49x^2 - 28x + 4$$. 4. **Substitute expansions back into the expression:** $$70x^2 - 62x + 12 - (49x^2 - 28x + 4)$$ 5. **Simplify by distributing the minus sign and combining like terms:** $$70x^2 - 62x + 12 - 49x^2 + 28x - 4 = (70x^2 - 49x^2) + (-62x + 28x) + (12 - 4)$$ $$= 21x^2 - 34x + 8$$ 6. **Factorise the quadratic $21x^2 - 34x + 8$:** - Find two numbers that multiply to $$21 \times 8 = 168$$ and add to $$-34$$. - These numbers are $$-28$$ and $$-6$$. 7. **Rewrite the middle term:** $$21x^2 - 28x - 6x + 8$$ 8. **Factor by grouping:** $$7x(3x - 4) - 2(3x - 4)$$ 9. **Factor out the common binomial:** $$(7x - 2)(3x - 4)$$ **Final answer:** $$\boxed{(7x - 2)(3x - 4)}$$