Given:The given expression is $(x+2y)^2-4(2x-y)^2$.To do:We have to factorize the expression $(x+2y)^2-4(2x-y)^2$.Solution:Factorizing algebraic expressions:Factorizing an algebraic expression means writing the expression as a product of two or more factors. Factorization is the reverse of distribution. An algebraic expression is factored completely when it is written as a product of prime factors.$(x+2y)^2-4(2x-y)^2$ can be written as, $(x+2y)^2-4(2x-y)^2=(x+2y)^2-[2(2x-y)]^2$             [Since $4=2^2$]Here, we can observe that the given expression is a difference of two squares. So, by using the formula $a^2-b^2=(a+b)(a-b)$, we can factorize the given expression. Therefore, $(x+2y)^2-4(2x-y)^2=(x+2y)^2-[2(2x-y)]^2$$(x+2y)^2-4(2x-y)^2=[(x+2y)+2(2x-y)][(x+2y)-2(2x-y)]$$(x+2y)^2-4(2x-y)^2=[(x+2y)+2(2x)-2(y)][(x+2y)-2(2x)+2(y)]$$(x+2y)^2-4(2x-y)^2=(x+2y+4x-2y)(x+2y-4x+2y)$$(x+2y)^2-4(2x-y)^2=(5x)(4y-3x)$Hence, the given expression can be factorized as $5x(4y-3x)$.Read More

Given:The given algebraic expression is $(2a-b)^2-16c^2$.To do:We have to factorize the expression $(2a-b)^2-16c^2$.Solution:Factorizing algebraic expressions:Factorizing an algebraic expression implies writing the expression as a product of two or more factors. Factorization is the reverse of distribution. An algebraic expression is factored completely when it is written as a product of prime factors.$(2a-b)^2-16c^2$ can be written as, $(2a-b)^2-16c^2=(2a-b)^2-(4c)^2]$             [Since $16=4^2$]Here, we can observe that the given expression is a difference of two squares. So, by using the formula $a^2-b^2=(a+b)(a-b)$, we can factorize the given expression. Therefore, $(2a-b)^2-16c^2=(2a-b)^2-(4c)^2$$(2a-b)^2-16c^2=(2a-b+4c)(2a-b-4c)$Hence, the given expression can be factorized as $(2a-b+4c)(2a-b-4c)$.Read More

Given:The given expression is $144a^2-169b^2$.To do:We have to factorize the expression $144a^2-169b^2$.Solution:Factorizing algebraic expressions:Factorizing an algebraic expression means writing the expression as a product of two or more factors. Factorization is the reverse of distribution. An algebraic expression is factored completely when it is written as a product of prime factors.$144a^2-169b^2$ can be written as, $144a^2-169b^2=(12a)^2-(13b)^2]$             [Since $144=(12)^2, 169=(13)^2$]Here, we can observe that the given expression is a difference of two squares. So, by using the formula $a^2-b^2=(a+b)(a-b)$, we can factorize the given expression. Therefore, $144a^2-169b^2=(12a)^2-(13b)^2$$144a^2-169b^2=(12a+13b)(12a-13b)$Hence, the given expression can be factorized as $(12a+13b)(12a-13b)$.Read More

Given:The given algebraic expression is $125x^2-45y^2$.To do:We have to factorize the expression $125x^2-45y^2$.Solution:Factorizing algebraic expressions:Factorizing an algebraic expression implies writing the expression as a product of two or more factors. Factorization is the reverse of distribution. An algebraic expression is factored completely when it is written as a product of prime factors.$125x^2-45y^2$ can be written as, $125x^2-45y^2=5[25x^2-9y^2]$                (Taking $5$ as common)$125x^2-45y^2=5[(5x)^2-(3y)^2]$             [Since $25=5^2, 9=3^2$]Here, we can observe that the given expression is a difference of two squares. So, by using the formula $a^2-b^2=(a+b)(a-b)$, we can factorize the given expression. Therefore, $125x^2-45y^2=5[(5x)^2-(3y)^2]$$125x^2-45y^2=5(5x+3y)(5x-3y)$Hence, ... Read More

Given:The given expression is $12m^2-27$.To do:We have to factorize the expression $12m^2-27$.Solution:Factorizing algebraic expressions:Factorizing an algebraic expression means writing the expression as a product of two or more factors. Factorization is the reverse of distribution. An algebraic expression is factored completely when it is written as a product of prime factors.$12m^2-27$ can be written as, $12m^2-27=3[4m^2-9]$                (Taking $3$ as common)$12m^2-27=3[(2m)^2-(3)^2]$             [Since $4=2^2, 9=3^2$]Here, we can observe that the given expression is a difference of two squares. So, by using the formula $a^2-b^2=(a+b)(a-b)$, we can factorize the given expression. Therefore, $12m^2-27=3[(2m)^2-(3)^2]$$12m^2-27=3(2m+3)(2m-3)$Hence, the ... Read More

Given:The given algebraic expression is $144a^2-289b^2$.To do:We have to factorize the expression $144a^2-289b^2$.Solution:Factorizing algebraic expressions:Factorizing an algebraic expression implies writing the expression as a product of two or more factors. Factorization is the reverse of distribution. An algebraic expression is factored completely when it is written as a product of prime factors.$144a^2-289b^2$ can be written as, $144a^2-289b^2=(12a)^2-(17b)^2]$             [Since $144=(12)^2, 289=(17)^2$]Here, we can observe that the given expression is a difference of two squares. So, by using the formula $a^2-b^2=(a+b)(a-b)$, we can factorize the given expression. Therefore, $144a^2-289b^2=(12a)^2-(17b)^2$$144a^2-289b^2=(12a+17b)(12a-17b)$Hence, the given expression can be factorized as $(12a+17b)(12a-17b)$.Read More

Given:The given expression is $27x^2-12y^2$.To do:We have to factorize the expression $27x^2-12y^2$.Solution:Factorizing algebraic expressions:Factorizing an algebraic expression means writing the expression as a product of two or more factors. Factorization is the reverse of distribution. An algebraic expression is factored completely when it is written as a product of prime factors.$27x^2-12y^2$ can be written as, $27x^2-12y^2=3[9x^2-4y^2]$                (Taking $3$ as common)$27x^2-12y^2=3[(3x)^2-(2y)^2]$             [Since $9=3^2, 4=2^2$]Here, we can observe that the given expression is a difference of two squares. So, by using the formula $a^2-b^2=(a+b)(a-b)$, we can factorize the given expression. Therefore, $27x^2-12y^2=3[(3x)^2-(2y)^2]$$27x^2-12y^2=3(3x+2y)(3x-2y)$Hence, the ... Read More

Given:The given algebraic expression is $16x^2-25y^2$.To do:We have to factorize the expression $16x^2-25y^2$.Solution:Factorizing algebraic expressions:Factorizing an algebraic expression implies writing the expression as a product of two or more factors. Factorization is the reverse of distribution. An algebraic expression is factored completely when it is written as a product of prime factors.$16x^2-25y^2$ can be written as, $16x^2-25y^2=(4x)^2-(5y)^2$             [Since $16=4^2, 25=5^2$]Here, we can observe that the given expression is a difference of two squares. So, by using the formula $a^2-b^2=(a+b)(a-b)$, we can factorize the given expression. Therefore, $16x^2-25y^2=(4x)^2-(5y)^2$$16x^2-25y^2=(4x+5y)(4x-5y)$Hence, the given expression can be factorized as $(4x+5y)(4x-5y)$.Read More

Given:The given algebraic expression is $ab-a-b+1$.To do:We have to factorize the expression $ab-a-b+1$.Solution:Factorizing algebraic expressions:Factorizing an algebraic expression implies writing the expression as a product of two or more factors. Factorization is the reverse of distribution. An algebraic expression is factored completely when it is written as a product of prime factors.Here, we can factorize the expression $ab-a-b+1$ by grouping similar terms and taking out the common factors. The terms in the given expression are $ab, -a, -b$ and $1$.We can group the given terms as $ab, -a$ and $-b, 1$. Therefore, by taking $a$ as common in $ab, -a$ and $-1$ as common in $-b, ... Read More

Given:The given expression is $x^2-11xy-x+11y$.To do:We have to factorize the expression $x^2-11xy-x+11y$.Solution:Factorizing algebraic expressions:Factorizing an algebraic expression means writing the expression as a product of two or more factors. Factorization is the reverse of distribution. An algebraic expression is factored completely when it is written as a product of prime factors.Here, we can factorize the expression $x^2-11xy-x+11y$ by grouping similar terms and taking out the common factors. The terms in the given expression are $x^2, -11xy, -x$ and $11y$.We can group the given terms as $x^2, -11xy$ and $-x, 11y$. Therefore, by taking $x$ as common in $x^2, -11xy$ and $-1$ as common in $-x, 11y$, ... Read More