Algebraic manipulation：練習問題

Simplify the expression \(7a + 4b - 3a + b\).

Factorise the expression \( 4a^2 - 12ab + 9b^2 \) fully.

Expand and simplify \((2x - 3)(x + 5) - (x + 2)^2\).

Simplify the expression $$3(2x - 5y) - 2(x + 3y)$$.

Factorise completely \(6x^2y - 18xy^2\).

Simplify the expression \(8x - 3y + 2 - 5x + 7y - 9\).

Factorise completely the four-term expression \(x^2 + 5x - ax - 5a\).

Factorise the cubic expression \(2x^3 - 50x\) completely.

(a) Expand and simplify the expression \( (2x - 1)(x + 3)(x - 4) \).
(b) Express as a single fraction in its simplest form:
\( \frac{2x^2 - 5x - 3}{x^2 - 9} \div \frac{4x^2 - 1}{2x^2 + 6x} \)

Perform the following algebraic manipulations:

(a) Factorise completely: $$ 3x^2 - 12x $$

(b) Factorise completely: $$ y^2 - 16x^2 $$

(c) Express as a single fraction in its simplest form: $$ \frac{2}{x-3} - \frac{1}{x+2} $$