Solution: Given, $\text{1^{st} expression} = a^4 + a^2b^2 +b^4$ $\implies (a^2)^2 + (b^2)^2 + a^2b^2$ $\implies (a^2 + b^2)^2 - 2a^2b^2 + a^2b^2$ $\implies (a^2 + b^2)^2 - a^2b^2$ $\implies (a^2 + b^2 - (ab)^2$ [ Using $a^2 - b^2 = (a+b)(a-b)$ ] $\implies (a^2 +ab +b^2)(a^2 - ab + b^2)$ $\text{2^{nd} expression} = a^3 + b^3$ $\impli…

Find the HCF and LCM:   4(a⁴ - a²b²), 6(a³b - ab³), 96(a³b + b⁴) Solution: Here, 1st expression: $4(a^4 - a^2b^2)$ = $4a^2(a^2 - b^2)$ = $2×2×a^2(a +b)(a -b)$ 2nd expression: $6(a^3b - ab^3)$ $= 6ab(a^2 - b^2)$ $= 2×3×ab(a +b)(a -b)$ 3rd expression: ${96(a^3b +b^4)}$ $= 96×b(a^3 + b^3)$ $= 2×3×16×b(a+b)(a^2 - ab + b^2)$ Now, Highest…

Question: Find the HCF of the following expressions: (a+b)² -4ab, a³ -b³, and a² +ab -2b². Solution: Given, 1st expression: (a+b)² - 4ab = (a² +2ab +b²) - 4ab = (a² -2ab +b²) = (a)² -2*a*b + (b)² = (a -b)² = (a-b)(a-b) 2nd expression: (a³ - b³) = (a-b)(a² +ab +b²) 3rd expression: (a² +ab -2b²) = a² +(2-1)ab -2b² = a² +2ab -ab -2b² =…

Question: Find the HCF of the following expressions: a³ -1, and a⁴ +a² +1. Solution: Given, 1st expression: a³ -1 = a³ -1³ = (a-1)(a² +a +1) 2nd expression: a⁴ +a² +1 = (a²)² +1² +a² = (a² +1)² -2a² +a² = (a² +1)² - a² = (a² +1)² - (a)² = (a² +a +1)(a² -a +1) Now, Highest Common Factor (H.C.F.) = common factors only = (a² +a +1) Rel…

Question: Find the HCF between a²-b²-2a+1, and a²-ab-a. Solution: Given, 1st expression: a² -b² -2a +1 = (a² -2a +1²) -b² = (a-1)² - (b)² = (a -b -1)(a +b -1) 2nd expression: a² -ab -a = a (a -b -1) Now, Highest Common Factor (H.C.F.) = common factors only = (a -b -1) Related Notes and Solutions: Here is the Facebook  link  to the s…

Find the HCF : $9x^2-4y^2-8yz-4z^2, 4z^2-4y^2-9x^2-12xy, 9x^2+12xz+4z^2-4y^2$. This is a class 10 Question From H.C.F. chapter of Unit Algebra (Mathematics). All the steps for the solutions are mentioned in the  description below . If that's hard for you to navigate, you can always visit the facebook link given at the end of eve…

Find the HCF : $x^3y+y^4, x^4+x^2y^2+y^4, 2ax^3-2ax^2y+2axy^2$. This is a class 10 Question From H.C.F. chapter of Unit Algebra (Mathematics). All the steps for the solutions are mentioned in the  description below . If that's hard for you to navigate, you can always visit the facebook link given at the end of every posts. Solut…

Find the HCF : $x^3-1, x^4+x^2+1, x^3+1+2x^2+2x$. This is a class 10 Question From H.C.F. chapter of Unit Algebra (Mathematics). All the steps for the solutions are mentioned in the  description below . If that's hard for you to navigate, you can always visit the facebook link given at the end of every posts. Solution : Given , …

Find the HCF : $m^3-m^2-m+1, 2m^4-2m and 3m^2+3m-6$. This is a class 10 Question From H.C.F. chapter of Unit Algebra (Mathematics). All the steps for the solutions are mentioned in the  description below . If that's hard for you to navigate, you can always visit the facebook link given at the end of every posts. Solution : Given…

Find the HCF : $x^2-9, \;x^3-27\;and;\;x^2+x-12$. This is a class 10 Question From H.C.F. chapter of Unit Algebra (Mathematics). All the steps for the solutions are mentioned in the  description below .  If that's hard for you to navigate, you can always visit the facebook link given at the end of every posts. Solution : Given ,…

Find the HCF : $16x^4-4x^2-4x-1$ and $8x^3-1$. This is a class 10 Question From H.C.F. chapter of Unit Algebra (Mathematics). All the steps for the solutions are mentioned in the  description below .  If that's hard for you to navigate, you can always visit the facebook link given at the end of every posts. Solution : Given , $1…

Find the HCF : $x^4+4y^4$ and $2x^3y+4xy^3+4x^2y^2$. This is a class 10 Question From H.C.F. chapter of Unit Algebra (Mathematics). All the steps for the solutions are mentioned in the  description below .  If that's hard for you to navigate, you can always visit the facebook link given at the end of every posts. Solution : Give…

Find the HCF : $x^3-8y^3$ and $x^2+2xy+4y^2$. This is a class 10 Question From H.C.F. chapter of Unit Algebra (Mathematics). All the steps for the solutions are mentioned in the  description below . If that's hard for you to navigate, you can always visit the facebook link given at the end of every posts. Solution : Given , $1^…

Find the HCF : $4x^3+8x^2$ and $5x^3-20x$. This is a class 10 Question From H.C.F. chapter of Unit Algebra (Mathematics). All the steps for the solutions are mentioned in the  description below . If that's hard for you to navigate, you can always visit the facebook link given at the end of every posts. Solution : Given , $1^{st}…

Find the HCF : $x^2-y^2$ and $x^2+2xy+y^2$. This is a class 10 Question From H.C.F. chapter of Unit Algebra (Mathematics). All the steps for the solutions are mentioned in the  description below . If that's hard for you to navigate, you can always visit the facebook link given at the end of every posts.  Solution : Given , $1^{s…

Find the HCF: $a^2-2a$ and $a^4-8a$. This is a class 10 Question From H.C.F. chapter of Unit Algebra (Mathematics). All the steps for the solutions are mentioned in the  description below . If that's hard for you to navigate, you can always visit the facebook link given at the end of every posts.  Solution : Given , $1^{st}\; ex…