Algebraic Identity: (a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ac

Q. If a + b + c = 10 and ab + bc + ca = 24, then the value of
$a^2+b^2+c^{2}is$.

1. 50
2. 46
3. 48
4. 52

Q.

Find:
$(a+b+c)\times (a+b-c)=$

1. $a^2+2ab-c^2$

2. $a^2+4ab+b^2-c^2$

3. $a^2+2ab+b^2$

4. $a^2+2ab+b^2-c^2$

Q.

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

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

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

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

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

Q. The value of (-3)${}^3$ + (7)${}^3$ + (-4)${}^3$ is :

1. 252
2. 264
3. 121
4. 343

Q. If $a+b+c=9$ and $ab+bc+ca=26$, then the value of $a^2+b^2+c^2-3$ is _______.

1. 25
2. 29
3. 26
4. 28

Q. Simplify
(i) $(x^2-5)(x+5)+25$
(ii) $(a^2+5)(b^3+3)+5$
(iii) $(t+8^2)(t^2-s)$
(iv) $(a+b)(c-d)+(a-b)(c+d)+2(ac+bd)$
(v) $(x+y)(2x+y)+(x+2y)(x-y)$
(vi) $(x+y)(x^2-xy+y^2)$
(vii) $(1.5x-4y)(1.5x+4y+3)-4.5x+12y$
(viii) $(a+b+c)(a+b-c)$

Q. State True or False.

1. True
2. False

Q.

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

1. 94

2. 24

3. 48

4. 47