Year 10 Algebra 2.2 Factorising using common factors

WATCH THE LESSON PATH ON THE WEEBLY UNDER FACTORISING OR/AND READ THROUGH THIS POWERPOINT (the videos that work through the same concepts as in this powerpoint). COMPLETE QUESTIONS AS SET OUT IN THIS POWERPOINT, ANY QUESTIONS FROM Q1-Q4 NOT COMPLETED IN CLASS BECOME HOMEWORK.

INSTRUCTIONS:

Review

• Factorising is the reverse of expanding• A common factor is something that you can

divide 2 (or more) terms and still get a whole number.

• You can factorise expressions by finding the HCF (highest common factor) and writing this on the outside of brackets that contain the remaining terms

Example – finding the HCF

• What is the highest common factor between the two terms below?

6ab and 8a2c

The highest common factor would be 2a because 2 is the highest number we can divide both coefficients by (the numbers at the front of the terms), and a is the only pronumeral present in both.

Factorsing – using the HCF (Q1)• This time the terms have been written in an expression

6ab + 8a2cAnd you have been asked to factorise (put some brackets in)

We already know the HCF is 2a, this has to come out the front of the brackets

2a(? + ?)To fill in the missing numbers we need to ask

2a x ? = 6ab 2a x ? = 8a2c2a x 3b = 6ab 2a x 4ac = 8a2c

Our final factorised answer would then be written2a(3b + 4ac)

More examples

COMPLETE ALL THE QUESTIONS FROM CHAPTER 2.2 Q1(screenshot on next page for those without textbook)

Factorise the following expressions

Factorising by grouping (Q2)

Example: 2a(x + 3) - 2(x + 3)• When there are 2 brackets that are the same

(in this case x+3) to factorise the expression you need to write what is directly outside the brackets into a second bracket

(2a - 2)(x+3) is in factorised form

COMPLETE ALL THE QUESTIONS FROM CHAPTER 2.2 Q2(screenshot on next page for those without textbook)

Factorise the following expressions

Factorise – grouping in pairs (Q3)

2ax – 8ay – cx + 4cyFactorise 2ax – 8ay = 2a(x – 4y)Factorise – cx – 4cy = -c(x – 4y)2a(x – 4y) -c(x – 4y)Brackets are the same so factorise by grouping(2a – c)(x – 4y)This is now fully factorised.

These brackets must be the same for this to

work

COMPLETE ALL THE QUESTIONS FROM CHAPTER 2.2 Q3(screenshot on next page for those without textbook)

Factorise the following expressions by grouping pairs (see example on previous page)

COMPLETE ALL THE QUESTIONS FROM CHAPTER 2.2 Q4-7

COMPLETE THESE QUESTIONS FROM CHAPTER 2.2Make sure you show your working out. (Q8,Q9 and Q11 in your textbook)

Question AChoose any whole number. What happens when you multiply the numbers either side of it?For example, if you choose 7, work out 6×8. Repeat several times.Notice anything interesting? Convince yourself it always happens.

Question BWrite down three consecutive numbers, none of which is a multiple of 3. If you can't, explain why.

Question CChoose two factors of 120 which are coprime (they have a highest common factor of 1).Multiply them together and record the result. Repeat several times. Notice anything about your results? Start with numbers other than 120. Does the same thing always happen? Convince yourself.

Question DChoose any two consecutive even numbers. Multiply them together and record the result. Repeat several times. Notice anything interesting? Convince yourself it always happens.

FINAL CHALLENGETake any prime number greater than 3, square it and subtract one. Repeat several times.Notice anything interesting? Convince yourself it always happens.

EXTENSION – Answer each of the following questions before attempting the final challenge at the bottom of this page.