1. **Simplify the algebraic expressions:** i. Simplify $9x + 2y - 4z + 8y - 3x + 11z$ Combine like terms: $$9x - 3x + 2y + 8y - 4z + 11z = (9x - 3x) + (2y + 8y) + (-4z + 11z)$$ $$= 6x + 10y + 7z$$ ii. Simplify $5x^3 y^2 - 7xy + 21xy + 8x^2 y^3$ Combine like terms $-7xy + 21xy$: $$5x^3 y^2 + ( -7xy + 21xy ) + 8x^2 y^3 = 5x^3 y^2 + 14xy + 8x^2 y^3$$ 2. **Factorize the expressions:** i. Factorize $x^2 - 7x - 18$ Find two numbers that multiply to $-18$ and add to $-7$: $-9$ and $2$ $$x^2 - 7x - 18 = (x - 9)(x + 2)$$ ii. Factorize $a^2 - 49$ Recognize difference of squares: $$a^2 - 49 = (a - 7)(a + 7)$$ iii. Factorize $4ax - 12ay + 5bx - 20by$ Group terms: $$(4ax - 12ay) + (5bx - 20by)$$ Factor out common factors: $$4a(x - 3y) + 5b(x - 4y)$$ Note: Since $(x - 3y)$ and $(x - 4y)$ are different, no further factorization is possible. 3. **Remove brackets and simplify:** i. Simplify $(9x + 2y)(x + 3y)$ Use distributive property: $$9x \cdot x + 9x \cdot 3y + 2y \cdot x + 2y \cdot 3y = 9x^2 + 27xy + 2xy + 6y^2$$ Combine like terms $27xy + 2xy$: $$9x^2 + 29xy + 6y^2$$ **Final answers for Question 1:** - A.i: $6x + 10y + 7z$ - A.ii: $5x^3 y^2 + 14xy + 8x^2 y^3$ - B.i: $(x - 9)(x + 2)$ - B.ii: $(a - 7)(a + 7)$ - B.iii: $4a(x - 3y) + 5b(x - 4y)$ - C.i: $9x^2 + 29xy + 6y^2$