Multiplication of Algebraic Expressions
Example 1:
$$ \textup{Multiply}\; a \; \textup{by} \; b$$
Solution:
$$ a×b = ab$$
Example 2:
$$ \textup{Multiply}\; 4x \; \textup{by} \; 5$$
Solution:
$$ 4x×5 = 20x$$
Example 3:
$$ \textup{Multiply}\; 3 \; \textup{by} \; 8c$$
Solution:
$$ 3×8c = 24c$$
Example 4:
$$ \textup{Multiply}\; a^2 \; \textup{by} \; a^4$$
Solution:
$$ a^2×a^4 = aa×aaaa = aaaaaa = a^6$$
$$ \textup{OR}$$
$$ a^2×a^4 = a^{2+4} = a^6$$
Example 5:
$$ \textup{Multiply}\; 4b^3 \; \textup{by} \; 7b^2$$
Solution:
$$ 4b^3×7b^2=28b^{3+2} = 28b^5$$
Example 6:
$$ \textup{Multiply}\; 5y \; \textup{by} \; 3y^6$$
Solution:
$$ 5y×3y^6=15y^{1+6} = 15y^7$$
Example 7:
$$ \textup{Multiply}\; 8x^2 \; \textup{by} \; 10x^4$$
Solution:
$$ 8x^2×10x^4=80x^{2+4} =80x^6$$
Example 8:
$$ \textup{Multiply}\; 2a \; \textup{by} \; 3b$$
Solution:
$$ 2a×3b=6ab$$
Example 9:
$$ \textup{Multiply}\; 4x \; \textup{by} \; 5y^2$$
Solution:
$$ 4x×5y^2=20xy^2$$
Example 10:
$$ \textup{Multiply}\; 7m^3 \; \textup{by} \; 2n^2$$
Solution:
$$ 7m^3×2n^2=14m^3n^2$$
Example 11:
$$ \textup{Multiply}\; 5c^4 \; \textup{by} \; 9d^5$$
Solution:
$$ 5c^4×9d^5=45c^4d^5$$
Example 12:
$$ \textup{Multiply}\; xy \; \textup{by} \; xy$$
Solution:
$$ xy×xy=x^{1+1}y^{1+1}=x^2y^2$$
Example 13:
$$ \textup{Multiply}\; 2ax \; \textup{by} \; 4ax$$
Solution:
$$ 2ax×4ax=8a^{1+1}x^{1+1}=8a^2x^2$$
Example 14:
$$ \textup{Multiply}\; 3ab \; \textup{by} \; 6ac$$
Solution:
$$ 3ab×6ac=18a^{1+1}bc=18a^2bc$$
Example 15:
$$ \textup{Multiply}\; a^2b^3 \; \textup{by} \; a^4b^2$$
Solution:
$$ a^2b^3×a^4b^2=a^{2+4}b^{3+2}=a^6b^5$$
Example 16:
$$ \textup{Multiply}\; x^3y^4 \; \textup{by} \; x^5y^5$$
Solution:
$$ x^3y^4×x^5y^5=x^{3+5}y^{4+5}=x^8y^9$$
Example 17:
$$ \textup{Multiply}\; 3c^2d \; \textup{by} \; 4c^3d^2$$
Solution:
$$ 3c^2d×4c^3d^2=12c^{2+3}d^{1+2}=12c^5d^3$$
Example 18:
$$ \textup{Multiply}\; 12p^7q^8 \; \textup{by} \; p^5q^6$$
Solution:
$$ 12p^7q^8×p^5q^6=12p^{7+5}q^{8+6}=12p^{12}q^{14}$$
Example 19:
$$ \textup{Find the product of}\; x^3, \; x^2\; \textup{and} \; x^7$$
Solution:
$$ x^3×x^2×x^7= x^{3+2+7} = x^{12}$$
Example 20:
$$ \textup{Find the product of}\; 4a^2, \; 2a^5\; \textup{and} \; a^6$$
Solution:
$$ 4a^2×2a^5×a^6=8a^{2+5+6} =8a^{13}$$
Example 21:
$$ \textup{Find the product of}\; 5x, \; 7y\; \textup{and} \; 2z$$
Solution:
$$ 5x×7y×2z=70xyz$$
Example 22:
$$ \textup{Find the product of}\; 6x^2y^3, \; 3x^3y^5\; \textup{and} \; 2x^4y^2$$
Solution:
$$ 6x^2y^3×3x^3y^5×2x^4y^2=36x^{2+3+4}y^{3+5+2} =36x^9y^{10}$$
Example 23:
$$ \textup{Find the product of}\; 2a^3b^2, \; b^3c^4\; \textup{and} \; 5a^2c^6$$
Solution:
$$ 2a^3b^2×b^3c^4×5a^2c^6=10a^{3+2}b^{2+3}c^{4+6} =10a^5b^5c^{10}$$
Example 24:
$$ \textup{Find the product of}\; 3a^3, \; 4b^2\; \textup{and} \; 6c^7$$
Solution:
$$ 3a^3×4b^2×6c^7=72a^3b^2c^7$$