Find the product of algebraic expressions by successive multiplication. x 2 y 2 + y 2 z 2 , y 2 z 2 + z 2 x 2 , z 2 x 2 + x 2 y 2

The given algebraic expressions are x 2 y 2 + y 2 z 2 , y 2 z 2 + z 2 x 2 and z 2 x 2 + x 2 y 2 . We have to find the product of given algebraic expressions. To multiply two polynomials multiply each term of one polynomial by each term of the other polynomial. That is, x 2 y 2 + y 2 z 2 × y 2 z 2 + z 2 x 2 = x 2 y 2 y 2 z 2 + z 2 x 2 + y 2 z 2 y 2 z 2 + z 2 x 2 = x 2 y 2 × y 2 z 2 + x 2 y 2 × z 2 x 2 + y 2 z 2 × y 2 z 2 + z 2 x 2 × y 2 z 2 = x 2 y 2 × y 2 z 2 + x 2 y 2 × z 2 x 2 + y 2 z 2 × y 2 z 2 + z 2 x 2 × y 2 z 2 = x 2 z 2 + z 2 y 2 + y 4 z 4 + y 2 x 2 Now, x 2 z 2 + z 2 y 2 + y 4 z 4 + y 2 x 2 × z 2 x 2 + x 2 y 2 = x 2 z 2 z 2 x 2 + x 2 y 2 + z 2 y 2 z 2 x 2 + x 2 y 2 + y 4 z 4 z 2 x 2 + x 2 y 2 + y 2 x 2 z 2 x 2 + x 2 y 2 = z 2 x 2 × x 2 z 2 + x 2 y 2 × x 2 z 2 + z 2 x 2 × z 2 y 2 + x 2 y 2 × z 2 y 2 + y 4 z 4 × z 2 x 2 + y 4 z 4 × x 2 y 2 + z 2 x 2 × y 2 x 2 + x 2 y 2 × y 2 x 2 = z 2 x 2 × x 2 z 2 + x 2 y 2 × x 2 z 2 + z 2 x 2 × z 2 y 2 + x 2 y 2 × z 2 y 2 + y 4 z 4 × z 2 x 2 + y 4 z 4 × x 2 y 2 + z 2 x 2 × y 2 x 2 + x 2 y 2 × y 2 x 2 = 2 + x 4 y 2 z 2 + z 4 x 2 y 2 + x 2 z 2 y 4 + y 4 z 2 x 2 + y 2 x 2 z 4 + z 2 y 2 x 4 Hence, the product of the given algebraic expression is 2 + x 4 y 2 z 2 + z 4 x 2 y 2 + x 2 z 2 y 4 + y 4 z 2 x 2 + y 2 x 2 z 4 + z 2 y 2 x 4 .

E M B I B E

Ganitprabha (MATHEMATICS TEXT BOOK) Class 8>Chapter 4 - Multiplication and Division of Polynomials>Let's work out - 4.1>Q 2

MEDIUM

8th West Bengal Board

IMPORTANT

Earn 100

Find the product of algebraic expressions by successive multiplication.

$(a + b + c), (a - b + c), (a + b - c)$

Important Questions on Multiplication and Division of Polynomials

MEDIUM

8th West Bengal Board

IMPORTANT

Ganitprabha (MATHEMATICS TEXT BOOK) Class 8>Chapter 4 - Multiplication and Division of Polynomials>Let's work out - 4.1>Q 2

Find the product of algebraic expressions by successive multiplication.

$(\frac{2 p^{2}}{q^{2}} + \frac{5 p^{2}}{q^{2}}), (\frac{2 p^{2}}{q^{2}} - \frac{5 p^{2}}{q^{2}})$

MEDIUM

8th West Bengal Board

IMPORTANT

Ganitprabha (MATHEMATICS TEXT BOOK) Class 8>Chapter 4 - Multiplication and Division of Polynomials>Let's work out - 4.1>Q 2

Find the product of algebraic expressions by successive multiplication.

$(\frac{x^{2}}{y^{2}} + \frac{y^{2}}{z^{2}}), (\frac{y^{2}}{z^{2}} + \frac{z^{2}}{x^{2}}), (\frac{z^{2}}{x^{2}} + \frac{x^{2}}{y^{2}})$

MEDIUM

8th West Bengal Board

IMPORTANT

Ganitprabha (MATHEMATICS TEXT BOOK) Class 8>Chapter 4 - Multiplication and Division of Polynomials>Let's work out - 4.1>Q 3

The simplified value of $= a^{3} + a^{2} b + a^{2} c + 2 a b c - a c^{2} - a b^{2} - b^{3} + b^{2} c + b c^{2} - c^{3}$ is $k x^{3}$ . Then the value of $k$ is?