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

Given:The given algebraic expression is $axy+bcxy-az-bcz$.To do:We have to factorize the expression $axy+bcxy-az-bcz$.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 $axy+bcxy-az-bcz$ by grouping similar terms and taking out the common factors. The terms in the given expression are $axy, bcxy, -az$ and $-bcz$.We can group the given terms as $axy, bcxy$ and $-az, -bcz$. Therefore, by taking $xy$ as common in $axy, bcxy$ and $-z$ as common in $-az, ... Read More

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

Given:The given algebraic expression is $2ax+bx+2ay+by$.To do:We have to factorize the expression $2ax+bx+2ay+by$.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 $2ax+bx+2ay+by$ by grouping similar terms and taking out the common factors. The terms in the given expression are $2ax, bx, 2ay$ and $by$.We can group the given terms as $2ax, 2ay$ and $bx, by$. Therefore, by taking $2a$ as common in $2ax, 2ay$ and $b$ as common in $bx, ... Read More

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

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