CHAPTER 8 - ALGEBRAIC EXPRESSIONS AND IDENTITIES

Exercise 8.2

1. Find the product of the following pairs of monomials:
(i) \(4, 7p\)

\[ 4 \times 7p = 28p \]

Final answer: \(28p\)
(ii) \(-4p, 7p\)

\[ -4p \times 7p = -28p^2 \]

Final answer: \(-28p^2\)
(iii) \(-4p, 7pq\)

\[ -4p \times 7pq = -28p^2q \]

Final answer: \(-28p^2q\)
(iv) \(4p^3, -3p\)

\[ 4p^3 \times (-3p) = -12p^4 \]

Final answer: \(-12p^4\)
(v) \(4p, 0\)

\[ 4p \times 0 = 0 \]

Final answer: \(0\)
2. Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively:
(i) \((p, q)\)

Area of rectangle = length × breadth

\[ = p \times q = pq \]

Final answer: \(pq\)
(ii) \((10m, 5n)\)

Area of rectangle = length × breadth

\[ = 10m \times 5n = 50mn \]

Final answer: \(50mn\)
(iii) \((20x^2, 5y^2)\)

Area of rectangle = length × breadth

\[ = 20x^2 \times 5y^2 = 100x^2y^2 \]

Final answer: \(100x^2y^2\)
(iv) \((4x, 3x^2)\)

Area of rectangle = length × breadth

\[ = 4x \times 3x^2 = 12x^3 \]

Final answer: \(12x^3\)
(v) \((3mn, 4np)\)

Area of rectangle = length × breadth

\[ = 3mn \times 4np = 12mn^2p \]

Final answer: \(12mn^2p\)
3. Complete the table of products:
First monomial →
Second monomial ↓
\(2x\) \(-5y\) \(3x^2\) \(-4xy\) \(7x^2y\) \(-9x^2y^2\)
\(2x\) \(4x^2\) \(-10xy\) \(6x^3\) \(-8x^2y\) \(14x^3y\) \(-18x^3y^2\)
\(-5y\) \(-10xy\) \(25y^2\) \(-15x^2y\) \(20xy^2\) \(-35x^2y^2\) \(45x^2y^3\)
\(3x^2\) \(6x^3\) \(-15x^2y\) \(9x^4\) \(-12x^3y\) \(21x^4y\) \(-27x^4y^2\)
\(-4xy\) \(-8x^2y\) \(20xy^2\) \(-12x^3y\) \(16x^2y^2\) \(-28x^3y^2\) \(36x^3y^3\)
\(7x^2y\) \(14x^3y\) \(-35x^2y^2\) \(21x^4y\) \(-28x^3y^2\) \(49x^4y^2\) \(-63x^4y^3\)
\(-9x^2y^2\) \(-18x^3y^2\) \(45x^2y^3\) \(-27x^4y^2\) \(36x^3y^3\) \(-63x^4y^3\) \(81x^4y^4\)
4. Obtain the volume of rectangular boxes with the following length, breadth and height respectively:
(i) \(5a, 3a^2, 7a^4\)

Volume of rectangular box = length × breadth × height

\[ = 5a \times 3a^2 \times 7a^4 = 105a^{7} \]

Final answer: \(105a^{7}\)
(ii) \(2p, 4q, 8r\)

Volume of rectangular box = length × breadth × height

\[ = 2p \times 4q \times 8r = 64pqr \]

Final answer: \(64pqr\)
(iii) \(xy, 2x^2y, 2xy^2\)

Volume of rectangular box = length × breadth × height

\[ = xy \times 2x^2y \times 2xy^2 = 4x^{4}y^{4} \]

Final answer: \(4x^{4}y^{4}\)
(iv) \(a, 2b, 3c\)

Volume of rectangular box = length × breadth × height

\[ = a \times 2b \times 3c = 6abc \]

Final answer: \(6abc\)
5. Obtain the product of:
(i) \(xy, yz, zx\)

\[ xy \times yz \times zx = x^{2}y^{2}z^{2} \]

Final answer: \(x^{2}y^{2}z^{2}\)
(ii) \(a, -a^2, a^3\)

\[ a \times (-a^2) \times a^3 = -a^{6} \]

Final answer: \(-a^{6}\)
(iii) \(2, 4y, 8y^2, 16y^3\)

\[ 2 \times 4y \times 8y^2 \times 16y^3 = 1024y^{6} \]

Final answer: \(1024y^{6}\)
(iv) \(a, 2b, 3c, 6abc\)

\[ a \times 2b \times 3c \times 6abc = 36a^{2}b^{2}c^{2} \]

Final answer: \(36a^{2}b^{2}c^{2}\)
(v) \(m, -mn, mnp\)

\[ m \times (-mn) \times mnp = -m^{3}n^{2}p \]

Final answer: \(-m^{3}n^{2}p\)

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