Found 225 Articles for Class 8

Given:The given expression is $10m^3n^2 + 15m^4n - 20m^2n^3$.To do:We have to factorize the expression $10m^3n^2 + 15m^4n - 20m^2n^3$.Solution:GCF:A common factor of two or more numbers is a factor that is shared by the numbers. The greatest common factor (GCF) of those numbers is found by finding all common factors of the numbers and selecting the largest one.The terms in the given expression are $10m^3n^2, 15m^4n$ and $- 20m^2n^3$.The numerical coefficient of $10m^3n^2$ is $10$The numerical coefficient of $15m^4n$ is $15$The numerical coefficient of $- 20m^2n^3$ is $20$This implies, $10=2\times5$$15=3\times5$$20=2\times2\times5$GCF of $10, 15$ and $20$ is $5$The common variables in the given terms are ... Read More

Given:The given expression is $2x^3y^2 - 4x^2y^3 + 8xy^4$.To do:We have to factorize the expression $2x^3y^2 - 4x^2y^3 + 8xy^4$.Solution:GCF:A common factor of two or more numbers is a factor that is shared by the numbers. The greatest common factor (GCF) of those numbers is found by finding all common factors of the numbers and selecting the largest one.The terms in the given expression are $2x^3y^2, -4x^2y^3$ and $8xy^4$.The numerical coefficient of $2x^3y^2$ is $2$The numerical coefficient of $-4x^2y^3$ is $4$The numerical coefficient of $8xy^4$ is $8$This implies, $2=2\times1$$4=2\times2$$8=2\times2\times2$GCF of $2, 4$ and $8$ is $2$The common variables in the given terms are $x$ and $y$.The power ... Read More

Given:The given expression is $20x^3 - 40x^2 + 80x$.To do:We have to factorize the expression $20x^3 - 40x^2 + 80x$.Solution:GCF:A common factor of two or more numbers is a factor that is shared by the numbers. The greatest common factor (GCF) of those numbers is found by finding all common factors of the numbers and selecting the largest one.The terms in the given expression are $20x^3, - 40x^2$ and $80x$.The numerical coefficient of $20x^3$ is $20$The numerical coefficient of $- 40x^2$ is $40$The numerical coefficient of $80x$ is $80$This implies, $20=2\times2\times5$$40=2\times2\times2\times5$$80=2\times2\times2\times2\times5$GCF of $20, 40$ and $80$ is $2\times2\times5=20$The common variable in the given terms is $x$The power ... Read More

Given:The given expression is $72x^6y^7 - 96x^7y^6$.To do:We have to factorize the expression $72x^6y^7 - 96x^7y^6$.Solution:GCF:A common factor of two or more numbers is a factor that is shared by the numbers. The greatest common factor (GCF) of those numbers is found by finding all common factors of the numbers and selecting the largest one.The terms in the given expression are $72x^6y^7$ and $- 96x^7y^6$The numerical coefficient of $72x^6y^7$ is $72$The numerical coefficient of $- 96x^7y^6$ is $96$This implies, $72=2\times2\times2\times3\times3$$96=2\times2\times2\times2\times2\times3$GCF of $72$ and $96$ is $2\times2\times2\times3=24$The common variables in the given terms are $x$ and $y$The power of $x$ in $72x^6y^7$ is $6$The power of $x$ ... Read More

Given:The given expression is $20a^{12}b^2 - 15a^8b^4$.To do:We have to factorize the expression $20a^{12}b^2 - 15a^8b^4$.Solution:GCF:A common factor of two or more numbers is a factor that is shared by the numbers. The greatest common factor (GCF) of those numbers is found by finding all common factors of the numbers and selecting the largest one.The terms in the given expression are $20a^{12}b^2$ and $-15a^8b^4$The numerical coefficient of $20a^{12}b^2$ is $20$The numerical coefficient of $-15a^8b^4$ is $15$This implies, $20=2\times2\times5$$15=3\times5$GCF of $20$ and $15$ is $5$The common variables in the given terms are $a$ and $b$The power of $a$ in $20a^{12}b^2$ is $12$The power of $a$ ... Read More

Given:The given expression is $5x-15x^2$.To do:We have to factorize the expression $5x-15x^2$.Solution:GCF:A common factor of two or more numbers is a factor that is shared by the numbers. The greatest common factor (GCF) of those numbers is found by finding all common factors of the numbers and selecting the largest one.The terms in the given expression are $5x$ and $-15x^2$The numerical coefficient of $5x$ is $5$The numerical coefficient of $-15x^2$ is $15$This implies, $5=5\times1$$15=3\times5$GCF of $5$ and $15$ is $5$The common variable in the given terms is $x$The power of $x$ in $5x$ is $x$The power of $x$ in $-15x^2$ is $2$The monomial of ... Read More

Given:The given expression is $3x-9$.To do:We have to factorize the expression $3x-9$.Solution:GCF:A common factor of two or more numbers is a factor that is shared by the numbers. The greatest common factor (GCF) of those numbers is found by finding all common factors of the numbers and selecting the largest one.The terms in the given expression are $3x$ and $-9$The numerical coefficient of $3x$ is $3$The numerical coefficient of $-9$ is $9$This implies, $3=3\times1$$9=3\times3$GCF of $3$ and $9$ is $3$Therefore, $3x=3\times x$$-9=3\times(-3)$This implies, $3x-9=3(x-3)$Hence, the given expression can be factorized as $3(x-3)$.Read More

Given:The given expression is $3a^2b^2+4b^2c^2+12a^2b^2c^2$.To do:We have to find the greatest common factor of the terms in the given expression.Solution:GCF:A common factor of two or more numbers is a factor that is shared by the numbers. The greatest common factor (GCF) of those numbers is found by finding all common factors of the numbers and selecting the largest one.The terms in the given expression are $3a^2b^2, 4b^2c^2$ and $12a^2b^2c^2$.The numerical coefficient of $3a^2b^2$ is $3$The numerical coefficient of $4b^2c^2$ is $4$The numerical coefficient of $12a^2b^2c^2$ is $12$This implies, $3=3\times1$$4=2\times2$$12=2\times2\times3$GCF of $3, 4$ and $12$ is $1$The common variable in the given terms is $b$The power ... Read More

Given:The given expression is $2xyz+3x^2y+4y^2$.To do:We have to find the greatest common factor of the terms in the given expression.Solution:GCF:A common factor of two or more numbers is a factor that is shared by the numbers. The greatest common factor (GCF) of those numbers is found by finding all common factors of the numbers and selecting the largest one.The terms in the given expression are $2xyz, 3x^2y$ and $4y^2$.The numerical coefficient of $2xyz$ is $2$The numerical coefficient of $3x^2y$ is $3$The numerical coefficient of $4y^2$ is $4$This implies, $2=2\times1$$3=3\times1$$4=2\times2$GCF of $2, 3$ and $4$ is $1$The common variable in the given terms is $y$The power ... Read More

Given:The given expression is $5a^4+10a^3-15a^2$.To do:We have to find the greatest common factor of the terms in the given expression.Solution:GCF:A common factor of two or more numbers is a factor that is shared by the numbers. The greatest common factor (GCF) of those numbers is found by finding all common factors of the numbers and selecting the largest one.The terms in the given expression are $5a^4, 10a^3$ and $-15a^2$.The numerical coefficient of $5a^4$ is $5$The numerical coefficient of $10a^3$ is $10$The numerical coefficient of $-15a^2$ is $15$This implies, $5=5\times1$$10=2\times5$$15=3\times5$GCF of $5, 10$ and $15$ is $5$The common variable in the given term is $a$The power ... Read More