Given:The given algebraic expression is $xa^2+xb^2-ya^2-yb^2$.To do:We have to factorize the expression $xa^2+xb^2-ya^2-yb^2$.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.Here, we can factorize the expression $xa^2+xb^2-ya^2-yb^2$ by grouping similar terms and taking out the common factors. The terms in the given expression are $xa^2, xb^2, -ya^2$ and $-yb^2$.We can group the given terms as $xa^2, xb^2$ and $-ya^2, -yb^2$. Therefore, by taking $x$ as common in $xa^2, xb^2$ and $-y$ as common in ... Read More

Given:The given algebraic expression is $ax+ay-bx-by$.To do:We have to factorize the expression $ax+ay-bx-by$.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 $ax+ay-bx-by$ by grouping similar terms and taking out the common factors. The terms in the given expression are $ax, ay, -bx$ and $-by$.We can group the given terms as $ax, ay$ and $-bx, -by$. Therefore, by taking $a$ as common in $ax, ay$ and $-b$ as common in $-bx, ... Read More

Given:The given algebraic expression is $1+x+xy+x^2y$.To do:We have to factorize the expression $1+x+xy+x^2y$.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 $1+x+xy+x^2y$ by grouping similar terms and taking out the common factors. The terms in the given expression are $1, x, xy$ and $x^2y$.We can group the given terms as $1, x$ and $xy, x^2y$. Therefore, by taking $1$ as common in $1, x$ and $xy$ as common in $xy, ... Read More

Given:The given algebraic expression is $p^2q-pr^2-pq+r^2$.To do:We have to factorize the expression $p^2q-pr^2-pq+r^2$.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.Here, we can factorize the expression $p^2q-pr^2-pq+r^2$ by grouping similar terms and taking out the common factors. The terms in the given expression are $p^2q, -pr^2, -pq$ and $r^2$.We can group the given terms as $p^2q, -pq$ and $-pr^2, r^2$. Therefore, by taking $pq$ as common in $p^2q, -pq$ and $r^2$ as common in $-pr^2, ... Read More

Given:The given algebraic expression is $qr-pr+qs-ps$.To do:We have to factorize the expression $qr-pr+qs-ps$.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 $qr-pr+qs-ps$ by grouping similar terms and taking out the common factors. The terms in the given expression are $qr, -pr, qs$ and $-ps$.We can group the given terms as $qr, -pr$ and $qs, -ps$. Therefore, by taking $r$ as common in $qr, -pr$ and $s$ as common in $qs, ... Read More

Given:The given algebraic expression is $4(x+y)(3a-b)+6(x+y)(2b-3a)$.To do:We have to factorize the expression $4(x+y)(3a-b)+6(x+y)(2b-3a)$.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 $4(x+y)(3a-b)+6(x+y)(2b-3a)$ by taking out the common factors. The highest common factor(HCF) of an algebraic expression is the highest factor that can be divided into each of the terms with no remainder.The terms in the given expression are $4(x+y)(3a-b)$ and $6(x+y)(2b-3a)$.We can observe that $(x+y)$ is ... Read More

Given:The given algebraic expression is $(2x-3y)(a+b)+(3x-2y)(a+b)$.To do:We have to factorize the expression $(2x-3y)(a+b)+(3x-2y)(a+b)$.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 $(2x-3y)(a+b)+(3x-2y)(a+b)$ by taking out the common factors. The greatest common factor(HCF) of an algebraic expression is the greatest factor that can be divided into each of the terms with no remainder.The terms in the given expression are $(2x-3y)(a+b)$ and $(3x-2y)(a+b)$.We can observe that $(a+b)$ is ... Read More

Given:The given algebraic expression is $x^3(a-2b)+x^2(a-2b)$.To do:We have to factorize the expression $x^3(a-2b)+x^2(a-2b)$.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 $x^3(a-2b)+x^2(a-2b)$ by taking out the common factors. The highest common factor of an algebraic expression is the highest factor that can be divided into each of the terms with no remainder.The terms in the given expression are $x^3(a-2b)$ and $x^2(a-2b)$.We can observe that $(a-2b)$ is ... Read More

Given:The given algebraic expression is $-4(x-2y)^2+8(x-2y)$.To do:We have to factorize the expression $-4(x-2y)^2+8(x-2y)$.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 $-4(x-2y)^2+8(x-2y)$ by taking out the common factors. The highest common factor(HCF) of an algebraic expression is the highest factor that can be divided into each of the terms with no remainder.The terms in the given expression are $-4(x-2y)^2$ and $8(x-2y)$.We can observe that $(x-2y)$ is ... Read More

Given:The given algebraic expression is $a(x-y)+2b(y-x)+c(x-y)^2$.To do:We have to factorize the expression $a(x-y)+2b(y-x)+c(x-y)^2$.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.Here, we can factorize the expression $a(x-y)+2b(y-x)+c(x-y)^2$ by taking out the common factors. The greatest common factor of an algebraic expression is the greatest factor that can be divided into each of the terms with no remainder.The terms in the given expression are $a(x-y), 2b(y-x)$ and $c(x-y)^2$.We can write $2b(y-x)$ as, ... Read More