Question
What should be added to $4c (-a + b + c)$ to obtain $3a(a + b + c) - 2b(a – b + c)?$
✓
Answer
Let $x$ be added to the given expression
$4c(-a + b + c)$ to obtain $3a(a + b + c) - 2b(a - b + c)$
i.e., $4c(-a + b + c)$
$= 3a(a + b + c) - 2b(a + b + c)$
$x = 3a(a + b + c) - 2b(a - b + c) - 4c(-a + b + c)$
$ =3 a^2+3 a b+3 a c-2 b a+2 b^2-2 b c+4 c a-4 c b-4 c^2 $
$ x=3 a^2+a b+7 a c+2 b^2-6 b c-4 c^2 $
$4c(-a + b + c)$ to obtain $3a(a + b + c) - 2b(a - b + c)$
i.e., $4c(-a + b + c)$
$= 3a(a + b + c) - 2b(a + b + c)$
$x = 3a(a + b + c) - 2b(a - b + c) - 4c(-a + b + c)$
$ =3 a^2+3 a b+3 a c-2 b a+2 b^2-2 b c+4 c a-4 c b-4 c^2 $
$ x=3 a^2+a b+7 a c+2 b^2-6 b c-4 c^2 $
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Three cubes each of side $10\ cm$ are joined end to end. Find the surface area of the resultant figure.
→The sum of four consecutive numbers is 34. What are these numbers?
A dealer buys a wristwatch for Rs. $225$ and spends Rs. $15$ on its repairs. If he sells the same for Rs. $300$, find his percent.
→The following pie chart depicts the expenditure of a state government under different heads.
$i.$ If the total spending is $10$ crores, how much money was spent on roads?
$ii.$ How many times is the amount of money spent on education compared to the amount spent on roads?
$iii.$ What fraction of the total expenditure is spent on both roads and public welfare together?
→$i.$ If the total spending is $10$ crores, how much money was spent on roads?
$ii.$ How many times is the amount of money spent on education compared to the amount spent on roads?
$iii.$ What fraction of the total expenditure is spent on both roads and public welfare together?
Observe the following pattern:
$ 1^3=1 $
$ 1^3+2^3=(1+2)^2 $
$ 1^3+2^3+3^3=(1+2+3)^2 $
Write the next three rows and calculate the value of $1^3+2^3+3^3+\ldots+9^3+10^3$ by the above pattern.
→$ 1^3=1 $
$ 1^3+2^3=(1+2)^2 $
$ 1^3+2^3+3^3=(1+2+3)^2 $
Write the next three rows and calculate the value of $1^3+2^3+3^3+\ldots+9^3+10^3$ by the above pattern.
Which of the two rational numbers is greater in the given pair$?$
$\frac{7}{-9}\ \text{or}\ \frac{-5}{8}$
→$\frac{7}{-9}\ \text{or}\ \frac{-5}{8}$
Diagram of the adjacent picture frame has outer dimensions $= 24 cm \times 28 cm$ and inner dimensions $16 cm \times 20 cm$. Find the area of each section of the frame, if the width of each section is the same
→On what sum will the compound interest at $5\%$ per annum for $2$ years compounded annually be Rs. $164?$
→Find the smallest number by which $192$ must be divided to obtain a perfect cube.
→By using the formula, find the amount and compound interest on.
$Rs. 10240$ for $3$ years at $12\frac{1}{2}\%$ per annum compounded annually.
→$Rs. 10240$ for $3$ years at $12\frac{1}{2}\%$ per annum compounded annually.