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In this lesson, we will learn how to rewrite expressions by expanding, factoring, and simplifying and become familiar with some useful identities.

Q1:

Factorise fully 6 4 π₯ β 8 1 2 .

Q2:

Factor the expression π₯ β 4 9 2 .

Q3:

Factor π β 6 π π + 9 π ο¨ ο¨ .

Q4:

Factor π₯ + 6 π₯ + 9 2 .

Q5:

Determine which of the following expressions is equivalent to π β π π + π 2 2 .

Q6:

An identity is an equation that is true for all values of its variables.

For example, 2 ( π + π ) = 2 π + 2 π is an identity because it will be true for all values of π and π .

Expand and simplify οΉ π₯ β π¦ ο + ( 2 π₯ π¦ ) 2 2 2 2 .

Factor π₯ + 2 π₯ π¦ + π¦ 4 2 2 4 .

Is the equation οΉ π₯ + π¦ ο = οΉ π₯ β π¦ ο + ( 2 π₯ π¦ ) 2 2 2 2 2 2 2 an identity?

Substitute π₯ = 3 and π¦ = 2 into the identity ( π₯ + π¦ ) = ( π₯ β π¦ ) + ( 2 π₯ π¦ ) 2 2 2 2 2 2 2 to generate a Pythagorean triple.

Q7:

Answer the following questions for the brackets ( π₯ β π¦ ) ( π₯ + π¦ ) .

Expand the brackets ( π₯ β π¦ ) ( π₯ + π¦ ) .

Is the identity ( π₯ β π¦ ) ( π₯ + π¦ ) = π₯ β π¦ 2 2 true?

Q8:

Is the equation π₯ + π¦ π₯ + π¦ = π₯ + π¦ 2 2 an identity?

Q9:

Is the equation π₯ + π¦ π₯ + π¦ = π₯ + π¦ ο© ο© ο¨ ο¨ an identity?

Q10:

Is the equation π₯ + 8 π₯ + 1 3 = ( π₯ + 8 ) β 8 π₯ β 5 1 2 2 an identity?

Q11:

Factor the expression 4 π β 9 π 2 2 .

Q12:

Factorise fully π π β ( π π β 5 ) 2 2 2 .

Q13:

Factorise fully π ( π + 8 π ) β π ( π + 8 π ) 3 3 .

Q14:

Factorise fully ( 5 π β 3 ) β 3 6 2 .

Q15:

Expand and simplify ( 2 π₯ β 3 π¦ ) οΉ 5 π₯ β 5 π₯ π¦ β π¦ ο 2 2 .

Q16:

Write two equivalent expressions for the area of the following figure.

Q17:

Express the following using symbols: The product of 4 and 16 plus 11.

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