__Objective__

At the end of this lesson, students should be able to:

- Expand products of algebraic expressions.

Expanding an expression means writing it without brackets. When removing brackets, every term inside the bracket must be multiplied by whatever is outside the bracket.

Directed numbers are numbers with either a positive or a negative sign. When using these numbers in algebra, it is important that we follow the same rules as we would for normal directed number calculations.

**(Positive number) × / ÷ (Positive number) = (Positive number)**

**(Negative number) × / ÷ (Negative number) = (Positive number)**

**(Positive number) × / ÷ (Negative number) = (Negative number)**

**(Negative number) × / ÷ (Positive number) = (Negative number)**

So 8 (– 3y) = – 24xy and (– 8 (– 3y) = 24xy

__Example 1__

Expand the algebraic expression.

__Solution __

__Example 2__

Expand the algebraic expression**.**

__Solution __

__Example 3__

Expand the algebraic expression:

__Solution__

__Example 4__

Expand the algebraic expression – 4x ( x – y + z^{2}).

__Solution __

– 4x (x – y + z^{2})

– 4x (x) – 4x(– y) – 4x (z^{2})

– 4x^{2} + 4xy – 4xz^{2}

__Example 5__

Expand the algebraic expression: – 2a^{2} (a + 3b – ^{1}/_{a}).

__Solution __

– 2a^{2} (a + 3b – ^{1}/_{a})

– 2a^{2}(a) – 2a^{2}(3b) – 2a^{2} (– ^{1}/_{a})

– 2a^{3} – 6a^{2}b + 2a

__Example 6__

Expand the algebraic expression – ^{2}/_{x} (– x + 4y + 1/x).

__Solution __

– ^{2}/_{x} – (x + 4y + 1/x) = – ^{2}/_{x} (– x) – ^{2}/_{x} (4y) – ^{2}/_{x} (^{1}/_{x})

= 2 – ^{8y}/_{x} – ^{2}/x^{2}

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