Single Brackets (SQA National 5 Maths): Revision Note

(a) Expand  $4x\left(2x-3\right)$.

(b) Expand  $-7x\left(4-5y\right)$.

Answer:

Part (a)

 Multiply the $4x$ term outside the brackets by both terms inside the brackets

$4x\times 2x+4x\times \left(-3\right)$

Carry out the multiplications

$8x^2-12x$

Part (b)

Multiply the $-7x$ outside the brackets by both terms inside the brackets

$\left(-7x\right)\times 4+\left(-7x\right)\times \left(-5y\right)$

Carry out the multiplications

• Remember that multiplying two negatives gives a positive

$-28x+35xy$

(a) Expand and simplify  $2\left(x+5\right)+3x\left(x-8\right)$.

(b) Expand and simplify  $3x\left(x+2\right)-7\left(x-6\right)$.

Answer:

Part (a)

Expand each set of brackets separately

You can keep negative terms inside brackets

$2\times x+2\times 5+3x\times x+3x\times \left(-8\right)$

Carry out the multiplications

$2x+10+3x^2-24x$

Collect like terms (the 2x and the -24x)

$-22x+10+3x^2$

Part (b)

Expand each set of brackets separately

• Be careful: the second set of brackets has a -7 in front, not +7

 $3x\times x+3x\times 2+\left(-7\right)\times x+\left(-7\right)\times \left(-6\right)$

Carry out the multiplications

• Remember that multiplying two negatives gives a positive

$3x^2+6x-7x+42$

Collect like terms

$3x^2-x+42$