Expanding brackets and combining like terms: แบบฝึกหัด

Simplify the following expression by expanding brackets and combining like terms:
\(4(2x - 3y) - 3(x + 2y)\)

Simplify the following expression by expanding the brackets and combining like terms:
\(5a - 2[3(a - 2b) - (4b - a)]\)

Simplify the following expression:
\(\frac{1}{2}(4a - 8b) - \frac{2}{3}(6b - 9a) + a\)

Simplify the algebraic expression:
\(3(x + 2) + 4(2x - 1)\)

Simplify the expression: \(5a - [2b + 3(a - 2b) - 4a]\).

Expand and simplify the following algebraic expression:
\( 5(2a + 3b) - 4a \)

Expand the expression and combine the like terms:
\( 3(4x - 2y + 1) - 2(x + 5y - 4) \)

Consider the algebraic expression \(S = 4(3a - 2b + 5) - 3(2a + 4b - 1)\).
(a) Expand and simplify the expression \(S\).
(b) If \(a = 5\) and the value of \(S\) is \(37\), find the value of \(b\).

Consider the expression \( E = 5x(2x - 3y + 4) - 2(3x^2 - 4xy - 7x + 2) \).

(a) Expand and simplify the expression \( E \) by combining like terms.
(b) If \( x = -2 \) and \( y = 3 \), find the numerical value of the simplified expression obtained in part (a).
(c) A student claims that for any value of \( y \), if \( x = 1 \), the value of the expression is always 10. Determine whether the student is correct and show your working.