Question
Multiply the binomials $(2pq + 3q^2)$ and $(3pq - 2q^2)$
✓
Answer
Product of $(2pq + 3q^2)$ and $(3pq - 2q^2)$
$= (2pq + 3q^2)(3pq - 2q^2)$
$= 2pq(3pq - 2q^2) + 3q^2(3pq - 2q^2)$
$= 6p^2q^2- 4pq^3+ 9pq^3- 6q^4$
$= 6p^2q^2+ 5pq^3- 6q^4$
$= (2pq + 3q^2)(3pq - 2q^2)$
$= 2pq(3pq - 2q^2) + 3q^2(3pq - 2q^2)$
$= 6p^2q^2- 4pq^3+ 9pq^3- 6q^4$
$= 6p^2q^2+ 5pq^3- 6q^4$
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Repeater Machine:
Similarly, repeater machine is a hypothetical machine which automatically enlarges items several times. For example, sending a piece of wire through a $(x2^4)$ machine is the same as putting it through a $(x2)$ machine four times. So, if you send a $3\ cm$ piece of wire through a $(x2^4)$ machine, its length becomes $3 \times 2 \times 2 \times 2 \times 2 = 48\ cm$. It can also be written that a base $(2)$ machine is being applied $4$ times.
What will be the new length of a 4cm strip inserted in the machine?
→Similarly, repeater machine is a hypothetical machine which automatically enlarges items several times. For example, sending a piece of wire through a $(x2^4)$ machine is the same as putting it through a $(x2)$ machine four times. So, if you send a $3\ cm$ piece of wire through a $(x2^4)$ machine, its length becomes $3 \times 2 \times 2 \times 2 \times 2 = 48\ cm$. It can also be written that a base $(2)$ machine is being applied $4$ times.
What will be the new length of a 4cm strip inserted in the machine?
Find the square root of number by using the method of prime factorisation: $225$
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→Find the square root of $2304$ by Division method.
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→How many sides does a regular polygon have, if each of its interior angles is $165^{\circ}$?
→Subtract the first rational number from the second in the following: $\frac{-8}{33},\frac{-7}{22}$
→Verify the following: $-8\times\frac{-13}{12}=\frac{-13}{12}\times(-8)$
→Write down the number of vertices of the following figures: Tetrahedron.