Rachel's copy of Distributive law: expanding one set of brackets

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Question 1

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a)

Expand the expression $\var{pmult}(\var{pxcoeff}x+\var{pconstant})$ .

$x$ + Expected answer:

The number in front of the bracket is multiplying the bracketed term, that is, each term in the brackets.

For example, $3(5x+6)$ means $3\times (5x+6)$ which means $3\times 5x+3\times 6$ , and so expanding $3(5x+6)$ gives $15x+18$ .

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b)

Expand $\var{nmult}(\var{nxcoeff}a-\var{-nconstant})$ .

$a$ + Expected answer:

The number in front of the bracket is multiplying the bracketed term, that is, each term in the brackets. Further, recall that a negative multiplied by a negative is a positive.

For example, $-3(5a-6)$ means $-3\times (5a-6)$ which means $(-3)\times 5a+(-3)\times (-6)$ , and so expanding $3(5a+6)$ gives $-15a+18$ .

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c)

Expand $-(\var{cx}x-\var{-cy}y+\var{cc})$ .

$x$ + $y$ + Expected answer:

A negative sign in front of a bracket is a common way to signify $-1$ times the bracketed term. The result is that it changes the sign of everything in the brackets.

For example, $-(5x-y+6)$ means $-1\times (5x-y+6)$ which means $(-1)\times 5x+(-1)\times (-y)+(-1)\times 6$ , and so expanding $-(5x-y+6)$ gives $-5x+y-6$ .

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Advice

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Rachel's copy of Distributive law: expanding one set of brackets

a)

b)

c)

Advice