Found 225 Articles for Class 8

Given:The given expressions are:(i) $y^2+5y-36$(ii) $(a^2-5a)^2-36$(iii) $(a+7)(a-10)+16$To do:We have to factorize the given algebraic expressions.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 $y^2+5y-36$.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.$y^2+5y-36$ can be written as, $y^2+5y-36=y^2+9y-4y-36$              [Since ... Read More

Given:The given expressions are:(i) $a^2+2a-3$(ii) $a^2+14a+48$(iii) $x^2-4x-21$To do:We have to factorize the given algebraic expressions.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 $a^2+2a-3$.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.$a^2+2a-3$ can be written as, $a^2+2a-3=a^2+3a-a-3$              [Since ... Read More

Given:The given expressions are:(i) $x^2-22x+120$(ii) $x^2-11x-42$To do:We have to factorize the given algebraic expressions.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 $x^2-22x+120$.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.$x^2-22x+120$ can be written as, $x^2-22x+120=x^2-12x-10x+120$              [Since $-22x=-12x-10x$ ... Read More

Given:The given expressions are:(i) $a^2+3a-88$(ii) $a^2-14a-51$(iii) $x^2+14x+45$To do:We have to factorize the given algebraic expressions.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 $a^2+3a-88$.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.$a^2+3a-88$ can be written as, $a^2+3a-88=a^2+11a-8a-88$              [Since ... Read More

Given:The given expressions are:(i) $x^2+12x-45$(ii) $40+3x-x^2$To do:We have to factorize the given algebraic expressions.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 $x^2+12x-45$.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.$x^2+12x-45$ can be written as, $x^2+12x-45=x^2+15x-3x-45$              [Since $12x=15x-3x$ ... Read More

Given:The given expressions are:(i) $49-x^2-y^2+2xy$(ii) $a^2+4b^2-4ab-4c^2$(iii) $x^2-y^2-4xz+4z^2$To do:We have to factorize the given algebraic expressions.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 $49-x^2-y^2+2xy$.$49-x^2-y^2+2xy$ can be written as, $49-x^2-y^2+2xy=49-(x^2+y^2-2xy)$$49-x^2-y^2+2xy=7^2-[(x)^2-2(x)(y)+(y)^2]$            [Since $49=7^2$ and $2xy=2(x)(y)$]Here, we can observe that the given expression is of the form $m^2-2mn+n^2$. So, by using the formula $(m-n)^2=m^2-2mn+n^2$, we can factorize the given expression.Here, $m=x$ and $n=y$ Therefore, $49-x^2-y^2+2xy=7^2-[(x)^2-2(x)(y)+(y)^2]$$49-x^2-y^2+2xy=7^2-(x-y)^2$Now, Using the formula ... Read More

Given:The given expressions are:(i) $25x^2-10x+1-36y^2$(ii) $a^2-b^2+2bc-c^2$(iii) $a^2+2ab+b^2-c^2$To do:We have to factorize the given algebraic expressions.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 $25x^2-10x+1-36y^2$.$25x^2-10x+1-36y^2$ can be written as, $25x^2-10x+1-36y^2=[(5x)^2-2(5x)(1)+(1)^2]-(6y)^2$                [Since $25x^2=(5x)^2, 10x=2(5x)(1)$ and $36y^2=(6y)^2$]Here, we can observe that the given expression is of the form $m^2-2mn+n^2$. So, by using the formula $(m-n)^2=m^2-2mn+n^2$, we can factorize the given expression.Here, $m=5x$ and $n=1$ Therefore, $25x^2-10x+1-36y^2=[(5x)^2-2(5x)(1)+(1)^2]-(6y)^2$$25x^2-10x+1-36y^2=(5x-1)^2-(6y)^2$Now, ... Read More

Given:The given expressions are:(i) $a^2-8ab+16b^2-25c^2$(ii) $x^2-y^2+6y-9$To do:We have to factorize the given algebraic expressions.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 $a^2-8ab+16b^2-25c^2$.$a^2-8ab+16b^2-25c^2$ can be written as, $a^2-8ab+16b^2-25c^2=[(a)^2-2(a)(4b)+(4b)^2]-(5c)^2$          [Since $8ab=2(a)(4b), 16b^2=(4b)^2$ and $25c^2=(5c)^2$]Here, we can observe that the given expression is of the form $m^2-2mn+n^2$. So, by using the formula $(m-n)^2=m^2-2mn+n^2$, we can factorize the given expression.Here, $m=a$ and $n=4b$ Therefore, $a^2-8ab+16b^2-25c^2=[(a)^2-2(a)(4b)+(4b)^2]-(5c)^2$$a^2-8ab+16b^2-25c^2=(a-4b)^2-(5c)^2$Now, Using the formula ... Read More

Given:The given expressions are:(i) $25-p^2-q^2-2pq$(ii) $x^2+9y^2-6xy-25a^2$(iii) $49-a^2+8ab-16b^2$To do:We have to factorize the given algebraic expressions.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 $25-p^2-q^2-2pq$.$25-p^2-q^2-2pq$ can be written as, $25-p^2-q^2-2pq=25-[p^2+2pq+q^2]$$25-p^2-q^2-2pq=5^2-[(p)^2+2(p)(q)+(q)^2]$             [Since $25=5^2$ and $2pq=2(p)(q)$]Here, we can observe that the given expression is of the form $m^2+2mn+n^2$. So, by using the formula $(m+n)^2=m^2+2mn+n^2$, we can factorize the given expression.Here, $m=p$ and $n=q$ Therefore, $25-p^2-q^2-2pq=5^2-[(p)^2+2(p)(q)+(q)^2]$$25-p^2-q^2-2pq=5^2-(p+q)^2$Now, Using the formula ... Read More

Given:The given expressions are:(i) $4x^4+1$.(ii) $4x^4+y^4$To do:We have to factorize the given algebraic expressions.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 $4x^4+1$.$4x^4+1$ can be written as, $4x^4+1=4x^4+1+4x^2-4x^2$                    (Add and subtract $4x^2$)$4x^4+1=[(2x^2)^2+2(2x^2)(1)+1^2]-4x^2$             [Since $4x^4=(2x^2)^2, 1=(1)^2$ and $4x^2=2(2x^2)(1)$]Here, we can observe that the given expression is of the form $m^2+2mn+n^2$. So, by using the formula ... Read More