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Year 7

Multiplying and simplifying with multiple expressions

I can use the distributive law to multiply multiple expressions by their respective terms and then simplify by collecting like terms

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New
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Year 7

Multiplying and simplifying with multiple expressions

I can use the distributive law to multiply multiple expressions by their respective terms and then simplify by collecting like terms

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Lesson details

Key learning points

  1. An expression can be multiplied by any term.
  2. We may have more than one expression being multiplied by terms.
  3. Collecting together like terms simplifies the expression.
  4. It is important to be methodical to avoid losing terms.

Keywords

  • Simplify - To simplify an expression is to write it in a more efficient and compact form without affecting the value of the original expression.

  • Like terms - Like terms are terms that have the same set of variables and corresponding exponents.

Common misconception

Pupils may think 5(y+1)-2(y+3) = 5y+5-2y+6

Correct use of the distributive law with either algebra tiles or an area model will demonstrate why this is wrong.

Assess students ability with the four operations with negative numbers beforehand to give students the best chance of success with this lesson.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
Without changing its value, we could write the expression $$5x+7+3x+8$$ more efficiently by it.
Correct Answer: simplifying
Q2.
Expand $$8(x+3)$$
$$8+x+3$$
Correct answer: $$8x+24$$
$$8x+3$$
$$x+24$$
Q3.
Match the expressions to the simplified expressions.
Correct Answer:$$3x + 7 + 4x + 6$$,$$7x +13$$

$$7x +13$$

Correct Answer:$$7x + 3 + 6x + 4$$,$$13x + 7$$

$$13x + 7$$

Correct Answer:$$7x + 13 + 3x -3$$,$$10x+10$$

$$10x+10$$

Correct Answer:$$6x -7 -13x -3 $$,$$-7x-10$$

$$-7x-10$$

Correct Answer:$$3x + 13 + 4x -3$$,$$7x+10$$

$$7x+10$$

Q4.
Match the expressions.
Correct Answer:$$7(y+3)$$,$$7y+21$$

$$7y+21$$

Correct Answer:$$-7(y-3)$$,$$21-7y$$

$$21-7y$$

Correct Answer:$$-7(y+3)$$,$$-7y-21$$

$$-7y-21$$

Correct Answer:$$7(y-3)$$,$$7y-21$$

$$7y-21$$

Q5.
Simplify $$10x+3-7x-10$$
$$3x+7$$
$$-3x+7$$
Correct answer: $$3x-7$$
$$-3x-7$$
Q6.
Expand $$-f(3e+2f-g)$$
$$-3e^2f-2f^2+fg$$
$$-3ef-f^2+fg$$
$$-3ef-2f^2-fg$$
Correct answer: $$-3ef-2f^2+fg$$

Exit quiz

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6 Questions

Q1.
In algebra, when we write the expression $$6(y-7)$$ as $$6y-42$$ it is called __________.
factorising
Correct answer: expanding
Correct answer: simplifying
dividing
Q2.
Expand $$-2x(5-x)$$
Correct answer: $$-10x+2x^2$$
$$3x-x$$
$$-10x-2x^2$$
$$10x+2x^2$$
Q3.
Expand and simplify $$2(y+3)+7(y-1)$$
$$2y+6-7y-7 \equiv -y-1$$
Correct answer: $$2y+6+7y-7 \equiv 9y-1$$
$$2y+6+7y-7 \equiv 9y+1$$
$$2y+3+7y-1 \equiv 9y+2$$
Q4.
Match the expressions.
Correct Answer:$$5(x+4)+3(x+8)$$,$$8x+44$$

$$8x+44$$

Correct Answer:$$5(x+4)+8(x+3)$$,$$13x+44$$

$$13x+44$$

Correct Answer:$$4(x+5)+3(x+8)$$,$$7x+44$$

$$7x+44$$

Correct Answer:$$4(x+5)+8(x-3)$$,$$12x-4$$

$$12x-4$$

Correct Answer:$$4(x-5)+8(x+3)$$,$$12x+4$$

$$12x+4$$

Q5.
Expand and simplify $$2d(d-3)-5(d+e)$$
$$2d^2+11d-5e$$
$$2d^2-8d-5e$$
$$2d^2-11d+5e$$
Correct answer: $$2d^2-11d-5e$$
Q6.
Match the expressions.
Correct Answer:$$x(x+y-7)-3x(x-2y)$$,$$-2x^2-7x+7xy$$

$$-2x^2-7x+7xy$$

Correct Answer:$$x(x+y-7)+3x(x-2y)$$,$$4x^2-7x-5xy$$

$$4x^2-7x-5xy$$

Correct Answer:$$-x(x+y-7)+3x(x-2y)$$,$$2x^2+7x-7xy$$

$$2x^2+7x-7xy$$

Correct Answer:$$-x(x+y-7)-3x(x-2y)$$,$$-4x^2+7x+5xy$$

$$-4x^2+7x+5xy$$