Simplify the following: 1 8 z x 2 y - 1 7 z 2 x y + 1 6 z y 2 x - 1 5 z y 2 x 2 - 1 4 x y z 2 + 1 3 x y 2 z - 1 2 x 2 y 2 z

The given expression is 1 8 z x 2 y - 1 7 z 2 x y + 1 6 z y 2 x - 1 5 z y 2 x 2 - 1 4 x y z 2 + 1 3 x y 2 z - 1 2 x 2 y 2 z For adding or subtracting algebraic expressions, we collect different groups of like terms and find the sums or differences in each group. Now, 1 8 z x 2 y - 1 7 z 2 x y + 1 6 z y 2 x - 1 5 z y 2 x 2 - 1 4 x y z 2 + 1 3 x y 2 z - 1 2 x 2 y 2 z = 1 8 x 2 y z - 1 7 x y z 2 - 1 4 x y z 2 + 1 6 x y 2 z + 1 3 x y 2 z - 1 5 x 2 y 2 z - 1 2 x 2 y 2 z = 1 8 x 2 y z - 1 7 + 1 4 x y z 2 + 1 6 + 1 3 x y 2 z - 1 5 + 1 2 x 2 y 2 z = 1 8 x 2 y z - 4 + 7 28 x y z 2 + 1 + 2 6 x y 2 z - 2 + 5 10 x 2 y 2 z = 1 8 x 2 y z - 11 28 x y z 2 - 1 2 x y 2 z - 7 10 x 2 y 2 z Hence, 1 8 z x 2 y - 1 7 z 2 x y + 1 6 z y 2 x - 1 5 z y 2 x 2 - 1 4 x y z 2 + 1 3 x y 2 z - 1 2 x 2 y 2 z = 1 8 x 2 y z - 11 28 x y z 2 - 1 2 x y 2 z - 7 10 x 2 y 2 z .

Find the following products: 5 z 6 × ( - 3 z 8 )

5 z 6 × - 3 z 8 = 5 × - 3 × z 6 × z 8 = - 15 z 6 + 8 = - 15 z 14

Find the following products: - 6 x 2 y z × 2 5 x y 3

Given, - 6 x 2 y z × 2 5 x y 3 = - 6 × 2 5 × x 2 × x × y × y 3 × z = - 12 5 × x 2 + 1 × y 1 + 3 × z = - 12 5 x 3 y 4 z

Find the following products: - 8 5 x 2 y z 3 × - 3 4 x y 2 z

Given, - 8 5 x 2 y z 3 × - 3 4 x y 2 z = - 8 5 × - 3 4 × x 2 x × y × y 2 × z 3 × z = 6 5 × x 2 + 1 × y 1 + 2 × z 3 + 1 = 6 5 x 3 y 3 z 4

Find the following products: 16 9 p q r × 9 8 p 3 q 2 r

Given, 16 9 × 9 8 × p × p 3 × q × q 2 × r × r = 2 × p 1 + 3 × q 1 + 2 × r 1 + 1 = 2 p 4 q 3 r 2

Find the following products: 50 3 a 2 b 2 × - 12 25 a b c

Give, 50 3 a 2 b 2 × - 12 25 a b c = 50 3 × - 12 25 × a 2 × a × b 2 × b × c = - 8 × a 1 + 2 × b 2 + 1 × c = - 8 a 3 b 3 c

E M B I B E

START UP MATHEMATICS>Chapter 5 - Algebraic Expressions and Identities: Part I>EXERCISE 5.2>Q 6

MEDIUM

8th CBSE

IMPORTANT

Earn 100

The two adjacent sides of the rectangular plot are $y - 6 x + 3 z + 8$ and $x - 2 y - 5 z - 8$ . Find the perimeter of the plot.

Important Questions on Algebraic Expressions and Identities: Part I

MEDIUM

8th CBSE

IMPORTANT

START UP MATHEMATICS>Chapter 5 - Algebraic Expressions and Identities: Part I>EXERCISE 5.2>Q 7

Simplify the following:

$(a - 3 b + 2 c) + (- 4 a + 9 b - 11 c) - (3 a - 4 b - 7 c)$

MEDIUM

8th CBSE

IMPORTANT

START UP MATHEMATICS>Chapter 5 - Algebraic Expressions and Identities: Part I>EXERCISE 5.2>Q 7

Simplify the following:

$\{7 - 2 x + 3 y - (3 x - y)\} - (2 x - 5 y + 11)$

HARD

8th CBSE

IMPORTANT

START UP MATHEMATICS>Chapter 5 - Algebraic Expressions and Identities: Part I>EXERCISE 5.2>Q 7

Simplify the following:

$\frac{1}{8} z x^{2} y - \frac{1}{7} z^{2} x y + \frac{1}{6} z y^{2} x - \frac{1}{5} z y^{2} x^{2} - \frac{1}{4} x y z^{2} + \frac{1}{3} x y^{2} z - \frac{1}{2} x^{2} y^{2} z$