Found 225 Articles for Class 8

Given:The given expression is $abx^2+(ay-b)x-y$.To do:We have to factorize the expression $abx^2+(ay-b)x-y$.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 $abx^2+(ay-b)x-y$ by grouping similar terms and taking out the common factors.We can write $abx^2+(ay-b)x-y$ as, $abx^2+(ay-b)x-y=abx^2+axy-bx-y$The terms in the given expression are $abx^2, ayx, -bx$ and $-y$.We can group the given terms as $abx^2, -bx$ and $axy, -y$. Therefore, by taking $bx$ as common in $abx^2, -bx$ and $y$ ... Read More

Given:The given algebraic expression is $x^3-2x^2y+3xy^2-6y^3$.To do:We have to factorize the expression $x^3-2x^2y+3xy^2-6y^3$.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 $x^3-2x^2y+3xy^2-6y^3$ by grouping similar terms and taking out the common factors. The terms in the given expression are $x^3, -2x^2y, 3xy^2$ and $-6y^3$.We can group the given terms as $x^3, 3xy^2$ and $-2x^2y, -6y^3$. Therefore, by taking $x$ as common in $x^3, 3xy^2$ and $-2y$ as common in $-2x^2y, ... Read More

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

Given:The given algebraic expression is $6xy+6-9y-4x$.To do:We have to factorize the expression $6xy+6-9y-4x$.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 $6xy+6-9y-4x$ by grouping similar terms and taking out the common factors. The terms in the given expression are $6xy, 6, -9y$ and $-4x$.We can group the given terms as $6xy, -4x$ and $6, -9y$. Therefore, by taking $2x$ as common in $6xy, -4x$ and $-3$ as common in $6, ... Read More

Given:The given expression is $x^3-y^2+x-x^2y^2$.To do:We have to factorize the expression $x^3-y^2+x-x^2y^2$.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 $x^3-y^2+x-x^2y^2$ by grouping similar terms and taking out the common factors. The terms in the given expression are $x^3, -y^2, x$ and $-x^2y^2$.We can group the given terms as $x^3, x$ and $-y^2, -x^2y^2$. Therefore, by taking $x$ as common in $x^3, x$ and $-y^2$ as common in $-y^2, -x^2y^2$, ... Read More

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