Expand And Simplify
One Set Of Double Brackets

Expansion And Simplification Of A Pair Of Binomials

Expansion And Simplification Of One Set Of Double Parentheses In Algebra

 

POSITIVE SIGNS ONLY IN THE CENTRE OF THE BRACKETS

Example 1  (x + 2)(x + 3)
   (x + 2)(x + 3)
= x(x + 3) + 2(x + 3)
= x(x) + x(3) + 2(x) + 2(3)
= x2 + 3x + 2x + 6
= x2 + 5x + 6

Example 2  (x + y)(x + y)
   (x + y)(x + y)
= x(x + y) + y(x + y)
= x(x) + x(y) + y(x) + y(y)
= x2 + xy + xy + y2
= x2 + 2xy + y2

 

POSITIVE AND NEGATIVE SIGNS IN THE CENTRE OF THE BRACKETS

Example 1  (x + 4)(x - 5)
   (x + 4)(x - 5)
= x(x - 5) + 4(x - 5)
= x(x) + x(-5) + 4(x) + 4(-5)
= x2 -5x + 4x -20
= x2 -x + 6

Example 2  (x - 3)(x + 2)
   (x - 3)(x + 2)
= x(x + 2) -3(x + 2)
= x(x) + x(2) -3(x) -3(2)
= x2 + 2x -3x -6
= x2 -x -6

Example 3  (x + y)(x - y)
   (x + y)(x - y)
= x(x - y) + y(x - y)
= x(x) + x(-y) + y(x) + y(-y)
= x2 - xy + xy - y2
= x2 - y2

Example 4  (a - b)(a + b)
   (a - b)(a + b)
= a(a + b) -b(a + b)
= a(a) + a(b) -b(a) -b(b)
= a2 + ab - ab - b2
= a2 - b2

 

NEGATIVE SIGNS ONLY IN THE CENTRE OF THE BRACKETS

Example  (x - 1)(x - 2)
   (x - 1)(x - 2)
= x(x - 2) -1(x - 2)
= x(x) + x(-2) -1(x) -1(-2)
= x2 -2x -x + 2
= x2 -3x + 2

 

FOIL METHOD
First Outer Inner Last

 

The Next Video Shows
Examples Done By Both The FOIL Method And By The Use Of A Table

 

SQUARING A BINOMIAL

 

SQUARING BRACKETS

 

 

 

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Edited by Dr David Cornelius an Independent Private Maths Tutor with over 25 years of experience and The Secretary of The Association of Tutors in the UK for 15 years.
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