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Algebraic Identity - Square of Sum of Binomial

Algebraic Identities - Concepts

Algebraic Identity - Square of Sum of Binomial

Algebraic Identity - Square of difference of Binomial

Algebraic Identity - Dfference of Square

Algebraic Identity -3

Algebraic Identity - Square of Trinomial

Class - 8th DAV Subjects

Concept Explanation

Algebraic Identity - Square of Sum of Binomial

The square of sum of two terms or the product of two same sum of terms is known as Square of Sum of Binomial and is popularly expressed in mathematical form

as either $small (a+b)^2 or (x+y)^2$ . If a and b are two terms, then the sum of binomial is expressed as a + b.

The square of sum of two terms identity is used as a formula in mathematics as.

The product of two same sum of binomials is expanded as sum of squares of the terms and twice the product of both terms. or it is stated as the summation of squares of two terms and two times the product of same terms is the square of sum of them.

Formula

$small (a+b)^2 = a^2+b^2+2ab$

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

Just like square of a number means multiplying the number with itself , square of a binomial means multiplying the binomial with itself . So,

${(a+b)^{2}} ={(a+b)}times {(a+b)}$

= $atimes (a+b)+btimes (a+b)$

= $a^{2}+ab+ba+b^{2$

= ${a^{2}}+2ab+{b^{2}}$

Illustration: Find the square of (2x+ 3y)

Solution:The square can be obtained by applying the identity where a denotes 2x and b denotes 3y

$(a+b)^2 = a^2+b^2+2ab$

Replacing a by 2x and b by 3y we get

$(2x+3y)^2 = (2x)^2+(3y)^2+2(2x)(3y)$

$=4x^2+9y^2+12xy$

Illustration: Find $(3x+4y)^{2}$ using Identity.

Solution:The square can be obtained by applying the identity where a denotes 3x and b denotes 4y

$(a+b)^2 = a^2+b^2+2ab$

Replacing a by 3x and b by 4y we get

${(3x+4y)^{2}}={(3x)^{2}}+ 2 times 3x times 4y+{(4y)^{2}}$

= $9x^{2}+24xy+16y^{2}$

Illustration: Evaluate $large (42)^{2}$ by using Identity.

Solution:The square of 42 can be obtained by expanding 42 as 40 + 2 and then applying the identity where a denotes 40 and b denotes 2

$(a+b)^2 = a^2+b^2+2ab$

Replacing a by 40 and b by 2 we get

$(42)^{2}$ = $(40+2)^{2}$

= $40^{2}+ 2 times 40 times 2+2^{2}$

= 1600 +160 +4 = 1764

Illustration: Evaluate $left ( x+frac{1}{x} right )^2$

Solution: The square can be obtained by applying the identity where a denotes x and b denotes 1/x

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Sample Questions

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Question : 1

â€‹â€‹â€‹â€‹â€‹â€‹Solve: $(2x+5)^2$
A. $4x^2+20x+2$	B. $4x^2+2x+25$	C. $4x^2+20x+25$	D. None of the above
Right Option : C
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Question : 2

Which of the following identities should be used to factorize $dpi{110} 9x^2+12xy+4y^2$
A. $dpi{110}(a+b)^2=a^2+b^2+2ab$	B. $(a+b)^3=a^2+b^2+3ab^2+3a^2b$	C. $(a-b)^2=a^2+b^2-2ab$	D. $a^2-b^2=(a-b)(a+b)$
Right Option : A
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Question : 3

Find square of $large dpi{110} fn_cm (9x^2+14y)$
A. $large dpi{110}81x^4+252x^2y+169y^4$	B. $large = 27x^4+196y^2 + 252x^2y$	C. $large dpi{110}81x^4+242x^2y+169y^2$	D. None of these
Right Option : B
View Explanation