Question

Find the product for the following expressions:

S.no	First Expression	Second Expression	Product
i)	$ a $	$ b + c + d $
ii)	$ x + y - 5 $	$ 5xy $
iii)	$ p $	$ 6{p^2} - 7p + 5 $
iv)	$ 4{p^2}{q^2} $	\[{p^2} - {q^2}\]
v)	\[a + b + c\]	\[abc\]

Answer 1

Hint: We are supposed to put each expression in brackets and then multiply each term in the first one with that of the second to obtain the product.

Complete step-by-step answer:
\[(a)(b + c + d)\]
Multiplying each term in subsequent bracket we get:
\[\] $ a \times b + a \times c + a \times d $ = $ ab + ac + ad $

 $ (x + y - 5)(5xy) $
Multiplying each subsequent term, we get:
 $ x \times 5xy + y \times 5xy - 5 \times 5xy $ = $ 5{x^2}y + 5x{y^2} - 25xy $

 $ (p)(6{p^2} - 7p + 5) $
Multiplying each subsequent term, we get:
                         \[p \times 6{p^2} - p \times 7p + p \times 5 = 6{p^3} - 7{p^2} + 5p\]
        iv) \[(4{p^2}{q^2})({p^2} - {q^2})\]
Multiplying each subsequent term, we get:
\[4{p^2}{q^2} \times {p^2} - 4{p^2}{q^2} \times {q^2} = 4{p^4}{q^2} - 4{p^2}{q^4}\]
[Power of like terms are added in multiplication]
v) \[(a + b + c)(abc)\]
            \[a \times abc + b \times abc + c \times abc = {a^2}bc + a{b^2}c + ab{c^2}\]

S.no	First Expression	Second Expression	Product
i)	$ a $	$ b + c + d $	$ ab + ac + ad $
ii)	$ x + y - 5 $	$ 5xy $	$ 5{x^2}y + 5x{y^2} - 25xy $
iii)	$ p $	$ 6{p^2} - 7p + 5 $	$ 6{p^3} - 7{p^2} + 5p $
iv)	$ 4{p^2}{q^2} $	\[{p^2} - {q^2}\]	\[4{p^4}{q^2} - 4{p^2}q4\]
v)	\[a + b + c\]	\[abc\]	\[{a^2}bc + a{b^2}c + ab{c^2}\]

Note: In multiplication, power of like terms are added.
\[({a^2} - {b^2}) = (a + b)(a - b)\] can also be used in (iv).
The constant of all terms have to multiplied and then written at the end result too for example 2x*3y it becomes 6xy.