Simplify 3(x+3) − 2x(x−1). Evaluate 4 1/2 × 4. Factorise completely 3a − c − 3ab + bc.

Question

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Here are the solutions to the problems:

1 Simplify $3(x+3) - 2x(x-1)$ .

Expand the terms by distributing.
$3(x+3) = 3x + 9$ $-2x(x-1) = -2x^2 + 2x$
Combine the expanded terms.
$3x + 9 - 2x^2 + 2x$
Group and combine like terms.
$-2x^2 + (3x + 2x) + 9$ $-2x^2 + 5x + 9$
The simplified expression is $\boxed{-2x^2 + 5x + 9}$ .

2 Evaluate $4^{\frac{1}{2}} \times 4$ .
Evaluate the fractional exponent.
$4^{\frac{1}{2}}$ is equivalent to $\sqrt{4}$ .
$\sqrt{4} = 2$
Perform the multiplication.
$2 \times 4 = 8$
The evaluated expression is $\boxed{8}$ .

3 Factorise completely $3a - c - 3ab + bc$ .
Rearrange the terms to group common factors.
$3a - 3ab - c + bc$
Factor out common terms from each pair of terms.
From the first pair ( $3a - 3ab$ ), factor out $3a$ :
$3a(1 - b)$
From the second pair ( $-c + bc$ ), factor out $-c$ :
$-c(1 - b)$
Factor out the common binomial factor $(1 - b)$ .
$(1 - b)(3a - c)$
The completely factorised expression is $\boxed{(1 - b)(3a - c)}$ .

Simplify 3(x+3) - 2x(x-1). Evaluate 4 1/2 x 4. Factorise completely 3a - c - 3ab + bc.