Home
Class 8
MATHS
Factorize each of the following algebrai...

Factorize each of the following algebraic expressions:
`49-a^2+8a b-16 b^2`
(2) `a^2-8a b+16 b^2-25 c^2`
(3) `x^2-y^2+6y-9`

Text Solution

Verified by Experts

(1) `49-a^2+8a b-16 b^2`
`= 49-(a^2-8ab+16b^2)`
`=7^2-(a-4b)^2`
By using the formula `(a^2-b^2)=(a+b)(a-b)`
`=(7+a-4b)(7-a+4b)`
`=(a-4b+7)(-a+4b+7)`

(2) `a^2-8a b+16 b^2-25 c^2`
`=(a-4b)^2-(5c)^2`
By using the formula `(a^2-b^2)=(a+b)(a-b)`
`=(a-4b+5c)(a-4b-5c)`

(3) `x^2-y^2+6y-9`
`=x^2+6y-(y^2-6y+9)`
`=x^2-(y-3)^2`
By using the formula `(a^2-b^2)=(a+b)(a-b)`
`=(x+y-3)(x-y+3)`
Promotional Banner

Topper's Solved these Questions

  • DIVISION OF ALGEBRAIC EXPRESSIONS

    RD SHARMA|Exercise All Questions|61 Videos

  • INTRODUCTION TO GRAPHS

    RD SHARMA|Exercise All Questions|31 Videos

Similar Questions

Explore conceptually related problems

Factorize each of the following expressions: 4a^(2)-9b^(2)-2a-3b

Factorize each of the following algebraic expressions: x^(2)-4x+4y-y^(2)( ii) 3-12(a-b)^(2)

Factorize each of the following algebraic expressions: x(x+z)-y(y+z)( ii) a^(2)-b^(2)-a-b

Factorize each of the following algebraic expressions: 16(2x-1)^(2)-25z^(2)4a^(2)-9b^(2)-2a-3b

Factorize each of the following expressions: x^(2)+2xy+y^(2)-a^(2)+2ab-b^(2)

Factorize each of the following expressions: 4a^(2)+12ab+9b^(2)-8a-12ba^(2)+b^(2)-2(ab-ac+bc)

Factorize each of the following expressions: 4a^(2)-9b^(2)-2a-3bx^(2)+2xy+y^(2)-a^(2)+2ab-b^(2)

Factorize each of the following algebraic expressions: a^(2)+2ab+b^(2)-c^(2)(2)49-x^(2)-y^(2)+2xya^(2)+4b^(2)-4ab-4c^(2)(4)x^(2)-y^(2)-4xz+4z^(2)

Factorize each of the following algebraic expressions: 4x^(2)+12xy+9y^(2)(2)9a^(2)-24ab+16b^(2)p^(2)-6pqr+9r^(2)(4)36a^(2)+36a+9a^(2)+2ab+b^(2)-16(6)9z^(2)-x^(2)+4xy-4y^(2)

Factorize each of the following algebraic expressions: 9a^(4)-24a^(2)b^(2)+16b^(4)-25616-a^(6)+4a^(3)b^(3)-4b^(6)a^(2)-2ab+b^(2)-c^(2)(4)x^(2)+2x+1-9y^(2)a^(2)+4ab+3b^(2)(6)96-4x-x^(2)