Found 225 Articles for Class 8

Given:The given quadratic polynomials are:(i) $4y^2+12y+5$(ii) $p^2+6p-16$To do:We have to factorize the given quadratic polynomials.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.Completing the square is a method that is used to write a quadratic expression in a way such that it contains the perfect square.(i) The given expression is $4y^2+12y+5$.We can write $4y^2+12y+5$ as, $4y^2+12y+5=4(y^2+3y+\frac{5}{4})$Here, The coefficient of $y^2$ is $1$The coefficient of $y$ is $3$The constant term is $\frac{5}{4}$Coefficient of ... Read More

Given:The given quadratic polynomials are:(i) $p^2+6p+8$(ii) $q^2-10q+21$To do:We have to factorize the given quadratic polynomials.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.Completing the square is a method that is used to write a quadratic expression in a way such that it contains the perfect square.(i) The given expression is $p^2+6p+8$.Here, The coefficient of $p^2$ is $1$The coefficient of $p$ is $6$The constant term is $8$Coefficient of $p^2$ is $1$. So, we ... Read More

Given:The given quadratic trinomials are:(i) $(x-2y)^2-5(x-2y)+6$(ii) $(2a-b)^2+2(2a-b)-8$To do:We have to factorize the given quadratic trinomials.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.(i) The given expression is $(x-2y)^2-5(x-2y)+6$.We can factorize the given expression by splitting the middle term. Splitting the middle term means we have to rewrite the middle term as the sum or difference of the two terms.Here, The coefficient of $(x-2y)^2$ is $1$The coefficient of $(x-2y)$ is $-5$The constant ... Read More

Given:The given quadratic trinomials are:(i) $36a^2+12abc-15b^2c^2$(ii) $15x^2-16xyz-15y^2z^2$To do:We have to factorize the given quadratic trinomials.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.(i) The given expression is $36a^2+12abc-15b^2c^2$.We can factorize the given expression by splitting the middle term. Splitting the middle term means we have to rewrite the middle term as the sum or difference of the two terms.Here, The coefficient of $a^2$ is $36$The coefficient of $a$ is $12bc$The constant ... Read More

Given:The given quadratic trinomials are:(i) $6x^2-13xy+2y^2$(ii) $14x^2+11xy-15y^2$(iii) $6a^2+17ab-3b^2$To do:We have to factorize the given quadratic trinomials.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.(i) The given expression is $6x^2-13xy+2y^2$.We can factorize the given expression by splitting the middle term. Splitting the middle term means we have to rewrite the middle term as the sum or difference of the two terms.Here, The coefficient of $x^2$ is $6$The coefficient of $x$ is $-13y$The ... Read More

Given:The given quadratic trinomials are:(i) $12x^2-17xy+6y^2$(ii) $6x^2-5xy-6y^2$To do:We have to factorize the given quadratic trinomials.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.(i) The given expression is $12x^2-17xy+6y^2$.We can factorize the given expression by splitting the middle term. Splitting the middle term means we have to rewrite the middle term as the sum or difference of the two terms.Here, The coefficient of $x^2$ is $12$The coefficient of $x$ is $-17y$The constant ... Read More

Given:The given quadratic trinomials are:(i) $11x^2-54x+63$(ii) $7x-6x^2+20$(iii) $3x^2+22x+35$To do:We have to factorize the given quadratic trinomials.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.(i) The given expression is $11x^2-54x+63$.We can factorize the given expression by splitting the middle term. Splitting the middle term means we have to rewrite the middle term as the sum or difference of the two terms.Here, The coefficient of $x^2$ is $11$The coefficient of $x$ is $-54$The ... Read More

Given:The given quadratic trinomials are:(i) $28-31x-5x^2$(ii) $3+23y-8y^2$To do:We have to factorize the given quadratic trinomials.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.(i) The given expression is $28-31x-5x^2$.We can factorize the given expression by splitting the middle term. Splitting the middle term means we have to rewrite the middle term as the sum or difference of the two terms.Here, The coefficient of $x^2$ is $-5$The coefficient of $x$ is $-31$The constant ... Read More

Given:The given quadratic trinomials are:(i) $3x^2+10x+3$(ii) $7x-6-2x^2$(iii) $7x^2-19x-6$To do:We have to factorize the given quadratic trinomials.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.(i) The given expression is $3x^2+10x+3$.We can factorize the given expression by splitting the middle term. Splitting the middle term means we have to rewrite the middle term as the sum or difference of the two terms.Here, The coefficient of $x^2$ is $3$The coefficient of $x$ is $10$The ... Read More

Given:The given quadratic trinomials are:(i) $2x^2+5x+3$(ii) $2x^2-3x-2$To do:We have to factorize the given quadratic trinomials.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.(i) The given expression is $2x^2+5x+3$.We can factorize the given expression by splitting the middle term. Splitting the middle term means we have to rewrite the middle term as the sum or difference of the two terms.Here, The coefficient of $x^2$ is $2$The coefficient of $x$ is $5$The constant ... Read More