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Practice — Maths 9 • Algebraic expressions

Algebraic expressions

Difficulty: ★★☆

1212

Simplify the expression a^2+6a-(a+2)^2. Write down the value of the expression when a=-3.

Your Answer:

-14

-10

-6

Solution:

\(a^2+6a-(a+2)^2=a^2+6a-(a^2+4a+4)=2a-4\).

When \(a=-3\): \(2\cdot(-3)-4=-6-4=-10\).

Algebraic expressions

Difficulty: ★★☆

1213

Simplify the expression (2a^2-6a)/(a-3)-4a+8. Write down the value of the expression when a=4.

Your Answer:

-8

Solution:

\(\dfrac{2a^2-6a}{a-3}=\dfrac{2a(a-3)}{a-3}=2a\) (for \(a\ne 3\)).

So the expression becomes \(2a-4a+8=-2a+8\).

When \(a=4\): \(-2\cdot4+8=0\).

Algebraic expressions

Difficulty: ★★☆

1214

Simplify the expression (a-3)^2-a(a-3). Write down the value of the expression when a=-4.

Your Answer:

-21

Solution:

Factor out \((a-3)\): \((a-3)^2-a(a-3)=(a-3)\big((a-3)-a\big)=(a-3)(-3)=-3a+9\).

When \(a=-4\): \(-3\cdot(-4)+9=12+9=21\).

Algebraic expressions

Difficulty: ★★☆

1215

Simplify the expression (2a^3-4a^2)/a^2 -7a+3. Write down the value of the expression when a=3.

Your Answer:

-12

-16

-10

Solution:

\(\dfrac{2a^3-4a^2}{a^2}=2a-4\) (for \(a\ne 0\)).

So the expression becomes \(2a-4-7a+3=-5a-1\).

When \(a=3\): \(-5\cdot3-1=-16\).

Algebraic expressions

Difficulty: ★★☆

1216

Simplify the expression (a-4)(a-3)-a^2+2a. Write down the value of the expression when a=-2.

Your Answer:

-22

Solution:

\((a-4)(a-3)=a^2-7a+12\).

Then \(a^2-7a+12-a^2+2a=-5a+12\).

When \(a=-2\): \(-5\cdot(-2)+12=10+12=22\).