Expansion of (x+y+z)^2

Q.

If a+b+c = 10 and $a^2+b^2+c^2=38;findab+bc+ca$

Q.

Find $a^2+b^2+c^2;ifa+b+c=9andab+bc+ca=24$

Q.

Find a+ b + c; if $a^2+b^2+c^2=83andab+bc+ca=71$

Q.

If $(a+b+c=25)$ and $(ab+bc+ca=59)$

Find the value of

$(a^2+b^2+c^2)$

1. 118

2. 500

3. 507

4. 527

Q.

Evaluate If a + b + c = 15 and $a^2+b^2+c^2$ = 125 , find ab + bc + ca

1. 100

2. 75

3. 81

4. 50

Q.

If a + b + c = 11 and $a^2+b^2+c^2=81$, find ; $ab+bc+ca$.

Q.

Find the square of $(2a+b)$.

Q.

Without actually calculating the cubes, find the value of ${(-12)}^3+{\left(7\right)}^3+{\left(5\right)}^3$.

1. -1260

2. 0

3. -36

4. -1620

Q.

If a + b + c = 9 and ab + bc + ca = 15, find : a^2 + b^2 + c^2.

Q. If ($ab+bc+ca)$ = 26 and $a^2+b^2+c^2$ = 29,
then ($a+b+c$) is :

1. 9
2. 18
3. 24
4. 12

Q.

Expand :

(i) $(2a+b{)}^2$

(ii) $(a-2b{)}^2$

(iii) ${(a+\frac{1}{2a})}^2$

(iv) ${(2a-\frac{1}{a})}^2$

(v) $(a+b-c{)}^2$

(vi) $(a-b+c{)}^2$

(vii) ${(3x+\frac{1}{3x})}^2$

(viii) ${(2x-\frac{1}{2x})}^2$

Q. Question 2(vii)
Simplify and express each of the following in exponential form:
(vii) $2^0\times 3^0\times 4^0$

Q.

Expand :

(i) $(3x-4y+5z{)}^2$

(ii) $(2a-5b-4c{)}^2$

(iii) $(5x+3y{)}^3$

(iv) $(6a-7b{)}^3$

Q. Expand: $(7m-3n-4k{)}^2$

Q.

If $a+b+c=11$ and $ab+bc+ac=32$
find
$a^2+b^2+c^2$

1. 57

2. 89

3. 45

4. 67

Q.

(a + b) (2a – 3b + c) – (2a – 3b) c = $2a^2$ – $2b^2$ – ab + 4bc – 2ac.

1. True

2. False

Q. Expand: $(3x-2b+5c{)}^2$

1. 

2. 

3. 

4. 

Q. $\text{Multiply}abc\text{with}(ab+bc+ac)$
$\text{and find its value for}a=1,b=0\text{and}c=2.$

1. 1
2. 0
3. -1
4. 2

Q. ${11}^3+{12}^3+{13}^3$ is divisible by

1. 11
2. 16
3. 13
4. 36

Q.

If $(a+b+c)$ is positive and $a^2+b^2+c^2=83$ and $ab+bc+ca=71$

then $a+b+c=$ ___

Q.

Expand the following identity.
​${(2x+1)}^3$

1. 

2. 

3. 

4. 

Q.

(a + b) (2a – 3b + c) – (2a – 3b) c = $2a^2$ – $2b^2$ – ab + 4bc – 2ac.

1. True

2. False

Q.

Find $a^2+b^2+c^2;ifa+b+c=9andab+bc+ca=24$

Q. If $f\left(x\right)=x^2+2bx+2c^2$ and $g\left(x\right)=-x^2-2cx+b^2$, such that minimum f(x) > maximum g(x), then the relation b and c, is

1. no real value of b and c
2. $0<c<b\sqrt{2}$
3. $|c|>|b|\sqrt{2}$
4. $|c|<|b|\sqrt{2}$

Q.

Which of the following equations are correct?

$\left(i\right)(a+b+c{)}^2=a^2+b^2+c^2-2(ab+bc+ca)$
$\left(ii\right)(a+b{)}^3=a^3+b^3+3ab(a-b)$
$\left(iii\right)(a-b{)}^3=a^3-b^3-3ab(a+b)$
$\left(iv\right)a^2-b^2=(a+b)(a-b)$

1. (i) and (iv)

2. (ii), (iii) and (iv)

3. (iv) only

4. (iv) and (iii)

Q.

If a + b + c = 0 ; then

(a^2 + b^2 + c^2) ÷ (ab +bc + ca) =

1. -2

2. 1

3. 2

4. 0

Q.

If a + b + c = 10 and a^2 + b^2 + c^2 = 38

then ab + bc + ca =

1. 31

2. 62

3. 0

4. 100

Q.

Expansion of $(2a+3b+4c{)}^2$ is ___________

1. $4a^2+9b^2+16c^2+12ab+24bc+16ca$

2. $a^2+b^2+2ca$

3. $a^2-b^2-2ca$

4. $a^2-b^2+2ca$

Q.

Evaluate $(a+2b+3c{)}^2$

1. $a^2+4b^2+9c^2+4ab+12bc+6ac$

2. $a^2+4b^2+9c^2+8ab+12bc+6ac$

3. $a^2+4b^2+9c^2+4ab+12bc+12ac$

4. $a^2+4b^2+9c^3+4ab+12bc+6ac$

Q. $(a-b)(b-c)+(b-c)(c-a)=$ ________

1. $a^2-b^2-c^2$
2. $2ab+2bc+2ac$
3. $2ab+2bc-2ac-a^2-b^2-c^2$
4. $2bc-2ac-b^2-c^2$