Identity (x+y+z)^2

Q. Expand $(x+2y+3z{)}^2$ using algebraic identity.

1. $x^2+4y^2+9z^2+2xy+2xz+3yz$
2. $x^2+4y^2+9z^2+xy+xz+yz$
3. $x^2+2y^2+3z^2+4xy+6xz+12yz$
4. $x^2+4y^2+9z^2+4xy+6xz+12yz$

Q.

Expand the following, using suitable identities: ${(-2x+3y+2z)}^2$

Q. Expand each of the following, using suitable identities:
(i) $(x+2y+4z{)}^2$
(ii) $(2x-y+z{)}^2$
(iii) $(-2x+3y+2z{)}^2$
(iv) $(3a-7b-c{)}^2$
(v) $(-2x+5y-3z{)}^2$
(vi) ${\left[\frac{1}{4}a-\frac{1}{2}b+1\right]}^2$

Q. If $x+y+z=10$ and $xy+yz+zx=20$, what is the value of $x^2+y^2+z^2$?

1. 40
2. 60
3. 80
4. 50

Q.

Find the following squares by using the identities ${(2xy+5y)}^2$.

Q.

Expand each of the following, using suitable identities: [3 MARKS]
$1){(x+2y+4z)}^2$
$2){(3x-7y-z)}^2$

Q. If $x-y+z=5$ and $x^2+y^2+z^2=49$, find the value of : $zx-xy-yz$

1. $-14$
2. $-12$
3. $12$
4. $14$

Q. If $x+y+z=10$ and $xy+yz+zx=20$, what is the value of $x^2+y^2+z^2$?

1. 40
2. 60
3. 80
4. 50

Q. Verify that $x^3+y^3+z^3-3xyz=\frac{1}{2}(x+y+z)\left[\right(x-y{)}^2+(y-z)+(z-x{)}^2]$

Q. State True or False.

1. True
2. False

Q. If $(x+y+z)=9$ and $(xy+yz+zx)=9$, then find the value of $(x^2+y^2+z^2)$.

1. $56$
2. $63$
3. $49$
4. $81$

Q. Evaluate : $(-12{)}^3+7^3+5^3$

Q. If $a+b+c=8$ and $ab+bc+ca=20$, then find the value of $a^3+b^3+c^3–3abc$.

1. 32

Q.

The expanded form of an expression is $x^2+y^2+z^2+2xy+2yz+2zx$. Which of the following is the expression?

1. ${(-x+y+z)}^2$
2. ${(x-y-z)}^2$
3. ${(x+y-z)}^2$
4. ${(x+y+z)}^2$