Lesson Learn to square binomials MENTALLY in just a MINUTE!

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Algebra: Polynomials, rational expressions and equations

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This Lesson (Learn to square binomials MENTALLY in just a MINUTE!) was created by by HyperBrain(694)

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this just a simple lesson.
This squaring has Two cases---- %28a%2Bb%29%5E2

%28a%2Bb%29%5E2

and

%28a-b%29%5E2

For the first case:
%28a%2Bb%29%5E2=a%5E2%2B2ab%2Bb%5E2

%28a%2Bb%29%5E2=a%5E2%2B2ab%2Bb%5E2

Example:
Find %282x%2B3y%29%5E2

%282x%2B3y%29%5E2

.

Here, a=2x and b=3y.
Furthermore,
a%5E2=%282x%29%5E2=4x%5E2

a%5E2=%282x%29%5E2=4x%5E2

b%5E2=%283y%29%5E2=9y%5E2

2ab=2%2A%282x%29%2A%283y%29=2%2A2%2A3%2Aa%2Ad=12xy

Thus,

2a%2B3d%29%5E2=4a%5E2%2B12ad%2B9d%5E2

SECOND CASE;
%28a-b%29%5E2=a%5E2-2ab%2Bb%5E2

%28a-b%29%5E2=a%5E2-2ab%2Bb%5E2

example:
Find %2812s-t%29%5E2

%2812s-t%29%5E2

.
Here, a=12s and b=t.
Furthermore,
a%5E2=%2812s%29%5E2=12%5E2%2As%5E2=144s%5E2

a%5E2=%2812s%29%5E2=12%5E2%2As%5E2=144s%5E2

b%5E2=t%5E2

2ab=2%2A12s%2At=24t

Thus,

%2812s-t%29%5E2=144s%5E2-24t%2Bt%5E2

TEST YOURSELF!
Find:
1. %28a-4r%29%5E2

%28a-4r%29%5E2

2.

%283e%2B3w%29%5E2

3.

%285g%2Br%29%5E2

you're done !

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