+1-415-670-9189

info@expertsmind.com

# Identities, Cube of a binomial, Algebra, Math Assignment Help

###
mathematics - Identities, Cube of a binomial, Algebra, Math

**Identity:** An identity is an equality which is true for all values of variables.

**IMPORTANT FORMULAE**

(1) To Find the Product (x + a) (x + b): (x + a) (x + b)

= x^{2} + (a + b)x + ab

Using this identity, we can derive the following results:

When b = a, we have

(x + a) (x + a) = x^{2} + 2ax + a^{2}

When = - a, we have = x^{2} - a^{2} When b = - b, we have

= x^{2} + (a - b)x - ab

When a = - a, we have = x^{2} + (b - a) x - ab

When a = - a, b = - b, we have = x^{2} - (a + b) x + ab.

(a + b)^{2} = a^{2} + 2ab + b^{2}

(a - b)^{2} = a^{2} - 2ab + b^{2}

(a + b) (a - b) = a^{2} - b^{2}.

To Find the Product (a + b) (a^{2} - ab + b^{2}): (a + b) (a^{2} - ab + b^{2})

= a^{3} + b^{3} To Find the Product (a - b)(a^{2} + ab + b^{2}) :

(a - b) (a^{2} + ab + b^{2}) = a^{3} - b^{3}

To Find the Product (a + b + c) (a^{2} + b^{2} + c^{2} - ab - bc - ac):

(a + b + c) (a^{2} + b^{2} + c^{2} - ab - bc - ac) = a^{3} + b^{3} + c^{3} - 3abc.

(2) **Cube of a binomial: **

(a + b)^{3} = a^{3} + b^{3} + 3ab (a + b)

a^{3} + b^{3} = (a + b)^{3} - 3ab (a + b)

(a - b)^{3} = a^{3} - b^{3} - 3ab (a - b)

a^{3} - b^{3} = (a - b)^{3} + 3ab (a - b).

(3) **Square of a trinomial: **

(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2ab + 2bc + 2ac.

**Note:** a, b, c may take various positive and negative values:

(i) (- a - b + c)^{2} = a^{2} + b^{2} + c^{2} + 2ab - 2ac - 2bc.

(ii) (a - b + c)^{2} = a^{2} + b^{2} + c^{2} - 2ab - 2bc + 2ac.

(iii) (- a + b + c)^{2} = a^{2} + b^{2} + c^{2} - 2ab + 2bc - 2ac.

(iv) (a - b - c)^{2} = a^{2} + b^{2} + c^{2} - 2ab + 2bc + 2ac.

(v) (a + b - c)^{2} = a^{2} + b^{2} + c^{2} + 2ab - 2bc - 2ac.

**An important result:** If a + b + c = 0, then a^{3} + b^{3} + c^{3} = 3abc.

We provide our students with a proficient service of Math Homework and Assignment related help. You just need to send your Math Assignment or Math Homework at our desired E-mail ID i.e. services@expertsmind.com or upload it at our website. Once our highly competent math tutors analyze your assignment, we will get back with an appropriate price quote. Then you have to make the payment through any of the various means listed on the website home page. At Expertsmind, delivery of every piece of work on time is given utmost priority and treated as a responsibility. We offer math assignment help & homework help service in very affordable price. We have instant math experts and instant math tutors for any grade level. We provide math homework help & math assignment help from school level, high school level to college or university exam level.

**Identity:**An identity is an equality which is true for all values of variables.

**IMPORTANT FORMULAE**

^{2}+ (a + b)x + ab

^{2}+ 2ax + a

^{2}

^{2}- a

^{2}When b = - b, we have

^{2}+ (a - b)x - ab

^{2}+ (b - a) x - ab

^{2}- (a + b) x + ab.

^{2}= a

^{2}+ 2ab + b

^{2}

^{2}= a

^{2}- 2ab + b

^{2}

^{2}- b

^{2}.

^{2}- ab + b

^{2}): (a + b) (a

^{2}- ab + b

^{2})

^{3}+ b

^{3}To Find the Product (a - b)(a

^{2}+ ab + b

^{2}) :

^{2}+ ab + b

^{2}) = a

^{3}- b

^{3}

^{2}+ b

^{2}+ c

^{2}- ab - bc - ac):

^{2}+ b

^{2}+ c

^{2}- ab - bc - ac) = a

^{3}+ b

^{3}+ c

^{3}- 3abc.

**Cube of a binomial:**

^{3}= a

^{3}+ b

^{3}+ 3ab (a + b)

^{3}+ b

^{3}= (a + b)

^{3}- 3ab (a + b)

^{3}= a

^{3}- b

^{3}- 3ab (a - b)

^{3}- b

^{3}= (a - b)

^{3}+ 3ab (a - b).

**Square of a trinomial:**

^{2}= a

^{2}+ b

^{2}+ c

^{2}+ 2ab + 2bc + 2ac.

**Note:**a, b, c may take various positive and negative values:

^{2}= a

^{2}+ b

^{2}+ c

^{2}+ 2ab - 2ac - 2bc.

^{2}= a

^{2}+ b

^{2}+ c

^{2}- 2ab - 2bc + 2ac.

^{2}= a

^{2}+ b

^{2}+ c

^{2}- 2ab + 2bc - 2ac.

^{2}= a

^{2}+ b

^{2}+ c

^{2}- 2ab + 2bc + 2ac.

^{2}= a

^{2}+ b

^{2}+ c

^{2}+ 2ab - 2bc - 2ac.

**An important result:**If a + b + c = 0, then a

^{3}+ b

^{3}+ c

^{3}= 3abc.