Harder Special Products And Factors-Chapter 6- Class 8- Advance Math

The Biotic World Provides Harder Special Products And Factors-Chapter 6- Class 8- Advance Math factor special products calculator, factoring special products worksheet answers, what do you want about special products and factoring, special products of binomials, factoring polynomials, factoring special cases worksheet pdf, algebraic expressions and special products, factoring special products part 2.

You will also get Harder Special Products And Factors-Chapter 6- Class 8- Advance Math, polynomial calculator, quadratic formula calculator, simplify calculator, algebra calculator, factor theorem calculator, factor by grouping, factoring trinomials, factoring calculator, mathway, factoring special products calculator, factoring special products answers, factoring special cases worksheet answers with work, factoring perfect square trinomials worksheet and many more.

Exercise- 6

1. Factorize

(i) (b+c)(c+a)(a+b)+abc

Solution:

(b+c)(c+a)(a+b)+abc

= (b+c){c(a+b)+a(a+b)}+abc

= (b+c)(ac+bc+ $\large a^{2}$ +ab)+abc

= (b+c)( $\large a^{2}$ +ab+ac+bc)+abc

= (b+c){ $\large a^{2}$ +a(b+c)+bc}+abc

= $\large a^{2}$ (b+c)+a(b+c)(b+c)+bc(b+c)+abc

= a(b+c){a+b+c}+bc{b+c+a}

= (a+b+c){a(b+c)+bc}

= (a+b+c)(ab+ac+bc)

(ii) a( $\large b^2$ - $\large c^2$ )+b( $\large c^2$ - $\large a^2$ )+c( $\large a^2$ - $\large b^2$ )

Solution:

a( $\large b^2$ - $\large c^2$ )+b( $\large c^2$ - $\large a^2$ )+c( $\large a^2$ - $\large b^2$ )

= a(b+c)(b-c)+b $\large c^2$ -b $\large a^2$ + $\large a^2$ c- $\large b^2$ c

= a(b+c)(b-c)+b $\large c^2$ - $\large b^2$ c-b $\large a^2$ + $\large a^2$ c

= a(b+c)(b-c)-bc(b-c)- $\large a^2$ (b-c)

= (b-c){a(b+c)-bc- $\large a^2$ }

= (b-c)(ab+ac-bc- $\large a^2$ )

= (b-c)<(- $\large a^2$ +ab+ac-bc)

= (b-c){-a(a-b)+c(a-b)}

= (b-c)(a-b)(c-a)

(iii) $\large y^2$ $\large z^2$ ( $\large y^2$ - $\large z^2$ )+ $\large z^2$ $\large x^2$ ( $\large z^2$ - $\large x^2$ )+ $\large x^2$ $\large y^2$ ( $\large x^2$ - $\large y^2$ )

Solution:

$\large y^2$ $\large z^2$ ( $\large y^2$ - $\large z^2$ )+ $\large z^2$ $\large x^2$ ( $\large z^2$ - $\large x^2$ )+ $\large x^2$ $\large y^2$ ( $\large x^2$ - $\large y^2$ )

$\large =y^2z^2(y+z)(y-z)+z^4x^2-z^2x^4+x^4y^2-x^2y^4$ $\large =y^2z^2(y+z)(y-z)-z^2x^4+x^4y^2+z^4x^2-x^2y^4$ $\large =y^2z^2(y+z)(y-z)+x^4(y^2-z^2)+x^2(z^4-y^4)$ $\large =y^2z^2(y+z)(y-z)+x^4(y^2-z^2)-x^2(y^4-z^4)$ $\large =y^2z^2(y+z)(y-z)+x^4(y+z)(y-z)-x^2(y^2+z^2)(y^2-z^2)$ $\large =(y+z)(y-z)\left \{ y^2z^2+x^4-x^2(y^2+z^2) \right \}$ $\large =(y+z)(y-z)\left \{ y^2z^2+x^4-x^2y^2-x^2z^2 \right \}$ $\large =(y+z)(y-z)\left \{ y^2z^2-x^2z^2-x^2y^2+x^4\right \}$ $\large =(y+z)(y-z)\left \{ z^2(y^2-x^2)-x^2(y^2-x^2)\right \}$ $\large =(y+z)(y-z)(y^2-x^2)(z^2-x^2)$

$\large =-(y+z)(y-z)(y+x)(y-x)(z+x)(z-x)$

$\large =(y+z)(y-z)(x+y)\left \{ -(x-y) \right \}(z+x)(z-x)$ $\large =-(y+z)(y-z)(x+y)(x-y)(z+x)(z-x)$

Harder Special Products And Factors-Chapter 6- Class 8- Advance Math

2 Comments

Contact form