Give Patterns And Example, Of, 1. Square Of Binomial, 2. Product Of The Sum And Difference Of Two Terms, 3. Square Of Trinomial, 4. Cube Of Binomial,

Give patterns and example

of
1. square of binomial
2. product of the sum and difference of two terms
3. square of trinomial
4. cube of binomial
5. product of a binomial and trinomial of the terms (2+b) (a squared + ab + b squared

 

1. Square of a Binomial

{(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2}

{(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2}

Example:

{(3x + 4)}^{2} = {9x}^{2} + 24x + 16

{(6x - 2y)}^{2} = 36 {x}^{2} - 24xy + 4 {y}^{2}

2. Product of the Sum and Difference of Two Terms

(x + y)(x - y) = {x}^{2} - {y}^{2}

Example:

(2x + 5y)(2x - 5y) = {2x}^{2} - {5y}^{2}

3. Square of a Trinomial

{(x + y + z)}^{2} = {x}^{2} + {y}^{2} + {z}^{2} + 2xy + 2xz + 2yz

Example:

{(2x + 3y + 5z)}^{2} ={4x}^{2} + {9y}^{2} + {25z}^{2} + 12xy + 20xz + 30y

4. Cube of a Binomial

{(x + y)}^{3} = {x}^{3} + 3 {x}^{2}y + 3x {y}^{2} + {y}^{3}

Example:

{(4x + 6y)}^{3} = 64 {x}^{3} + 288 {x}^{2} y + 432x {y}^{2} + 216 {y}^{3}

5. Product of a Binomial and Trinomial

(x + y)(x + y + z) = {x}^{2} +2xy+xz+ {y}^{2} +yz

Example:

(2x + 3y)(2x + 3y + 4z) = {4x}^{2} +12xy+8xz+ {9y}^{2} 2+12yz


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