Expansion of (x+y+z)^2

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.

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.

If a + b + c = 0 ; then

(a^2 + b^2 + c^2) ÷ (ab +bc + ca) =

1. -2

2. 1

3. 2

4. 0

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.

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 $(x+y+z{)}^2$ :

1. $x^2+y^2+z^2+2(xy+yz+zx)$
2. $x^2+y^2+z^2-2(xy+yz+zx)$
3. $x^2+y^2+z^2-2(xy-yz+zx)$
4. $x^2+y^2+z^2+2(xy-yz+zx)$

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.

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

1. 

2. 

3. 

4. 

Q.

If a + b + c = 12 and $a^2+b^2+c^2=50$; find ab + bc + ca

1. (x+2)

2. (x + 2) (x + 3)

3. (x+3)

4. x(x+1)