Expand Difference of Squares Examples

1. Expand (x-6)(x+6) $(x-6)(x+6)$

Solution:

Using the identity, $"Using the identity,"$

(X+A)(X-A)=X2-A2 $(X+A)(X-A)=X^2-A^2$

Here X=x,A=-6 $"Here "X=x,A=-6$

=(x)2-(-6)2 $=(x)^2-(-6)^2$

=x2-36 $=x^2-36$

2. Expand (2x-5)(2x+5) $(2x-5)(2x+5)$

Solution:

Using the identity, $"Using the identity,"$

(X+A)(X-A)=X2-A2 $(X+A)(X-A)=X^2-A^2$

Here X=2x,A=-5 $"Here "X=2x,A=-5$

=(2x)2-(-5)2 $=(2x)^2-(-5)^2$

=4x2-25 $=4x^2-25$

3. Expand (3x-2)(3x+2) $(3x-2)(3x+2)$

Solution:

Using the identity, $"Using the identity,"$

(X+A)(X-A)=X2-A2 $(X+A)(X-A)=X^2-A^2$

Here X=3x,A=-2 $"Here "X=3x,A=-2$

=(3x)2-(-2)2 $=(3x)^2-(-2)^2$

=9x2-4 $=9x^2-4$

4. Expand (x-y)(x+y) $(x-y)(x+y)$

Solution:

Using the identity, $"Using the identity,"$

(X+A)(X-A)=X2-A2 $(X+A)(X-A)=X^2-A^2$

Here X=x,A=-y $"Here "X=x,A=-y$

=(x)2-(-y)2 $=(x)^2-(-y)^2$

=x2-y2 $=x^2-y^2$

5. Expand (x-2y)(x+2y) $(x-2y)(x+2y)$

Solution:

Using the identity, $"Using the identity,"$

(X+A)(X-A)=X2-A2 $(X+A)(X-A)=X^2-A^2$

Here X=x,A=-2y $"Here "X=x,A=-2y$

=(x)2-(-2y)2 $=(x)^2-(-2y)^2$

=x2-4y2 $=x^2-4y^2$

This material is intended as a summary. Use your textbook for detail explanation.
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