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In this lesson, we will learn how to simplify polynomials by expanding parentheses, multiplying by monomials, and adding and subtracting terms of the same power.

Q1:

Simplify οΉ 2 π₯ β 4 π₯ β 9 ο β οΉ 5 π₯ β 3 π₯ + 1 ο 3 2 3 .

Q2:

Simplify 6 ( 3 π + 2 ) + 4 ( 2 π + 4 ) .

Q3:

Simplify 6 οΉ 5 π§ + 2 ο β 2 ( π§ β 4 ) 2 .

Q4:

Factorise fully π β 1 4 π π + 4 8 π 4 2 2 4 .

Q5:

Express, in terms of π₯ , π¦ , and π§ , the sum of the surface areas of the two given figures.

Q6:

Q7:

Which of the following is equivalent to ( π₯ β π¦ ) ( π₯ + π¦ ) οΉ π₯ β 2 π₯ π¦ + π¦ ο 4 2 2 4 ?

Q8:

Is the equation π₯ β π¦ π₯ + π¦ = π₯ β π¦ 4 4 2 2 2 2 an identity?

Q9:

Is the equation π₯ + π¦ π₯ β π¦ = π₯ + π¦ 4 4 2 2 2 2 an identity?

Q10:

Simplify 6 π₯ ( π₯ + π¦ ) β π¦ ( 6 π₯ β π¦ ) + 6 ( π¦ β π₯ ) 6 6 7 7 .

Q11:

Simplify 8 π₯ ( π₯ + π¦ ) β π¦ ( 8 π₯ β π¦ ) + 8 ( π¦ β π₯ ) 7 7 8 8 .

Q12:

Simplify β 8 π₯ ( π₯ + π¦ ) β π¦ ( β 8 π₯ β π¦ ) β 8 ( π¦ β π₯ ) 7 7 8 8 .

Q13:

Expand and simplify 7 π₯ ( π₯ + π¦ ) + π¦ [ 3 π₯ β 4 π¦ ( π₯ + 2 π¦ ) ] + 7 π₯ [ 3 π₯ β 2 ( π₯ + 3 π¦ ) ] .

Q14:

Expand and simplify 4 π₯ ( π₯ β 6 π¦ ) + 6 π¦ [ 4 π₯ + 6 π¦ ( π₯ + π¦ ) ] β 2 π₯ [ π₯ + 5 ( π₯ β 2 π¦ ) ] .

Q15:

Expand and simplify 6 π₯ ( π₯ + 6 π¦ ) + 4 π¦ [ 4 π₯ β 3 π¦ ( 2 π₯ β 3 π¦ ) ] + 2 π₯ [ 4 π₯ + 5 ( π₯ + 5 π¦ ) ] .

Q16:

Find an expression for the area of the shape below.

Q17:

Q18:

Simplify 8 π₯ Γ 3 π¦ Γ 5 π§ .

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