Expansion of (a+b+c)^2

Q. If $a+b+c$ = 15 and $a^2+b^2+c^2$ = 77,
then ($ab+bc+ca)$ is :

1. 74
2. 72
3. 144
4. 148

Q. If $a+b+c=12$ and $a^2+b^2+c^2=50$, then ab + bc + ca = .

1. $84$
2. $88$
3. $47$
4. $94$

Q.

Prove the following identities :

$\left(i\right)(a+b{)}^2=a^2+b^2+2ab$

$\left(ii\right)(a-b{)}^2=a^2+b^2-2ab$ [2 MARKS]

Q.

Factorize the expression $125x^3+\frac{1}{8}$.

Q. Expand $(198{)}^3$

Q. The expansion of $(2x+y-5{)}^2$ is :

1. $4x^2+y^2+25+4xy-10y-20x$
2. $4x^2+y^2+75+4xy-10y-20x$
3. $4x^2+y^2+25+4xy-10y-10x$
4. $4x^2+y^2+25+4xy-20y-20x$

Q.

Question 4(b)
Simplify : $a(a^2+a+1)+5$ and find its value for (i) a=0 (ii) a=1 (iii) a=-1.

Q. Simplify: $(l+2m+n{)}^2+(l-2m+n{)}^2$

1. $(l^2+n^2+4m^2+2ln)$
2. $(l^3+n^2+2m^2+4ln)$
3. $2(l^2+n^2-4m^2-2ln)$
4. $2(l^2+n^2+4m^2+2ln)$

Q. The expansion of $(x+2y+3z{)}^2$ is :

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

Q.

The product of ( $l$ + $m$ ) and ( $l$ - $m$ ) can be written as ______ .

1. 2lm

2. l² + m²

3. l² - m²

4. 2l² - 2m²

Q. The expansion of $(x+\frac{1}{x}+2{)}^2$ is :

1. $x^2+\frac{1}{x^2}+\frac{4}{x}+4x+6$
2. $x^2+\frac{1}{x^2}+\frac{4}{x}+8x+6$
3. $4x^2+\frac{1}{x^2}+\frac{4}{x}+4x+6$
4. $x^2+\frac{1}{x^2}+\frac{4}{x}+4x+4$

Q. Evaluate 9³ - 5³ - 4^{3 .}

1. 450
2. 180
3. 270
4. 540

Q. If $a+b+c=9$ and $2(ab+bc+ca)=52$,
then $a^2+b^2+c^2$ is _____.

1. 29
2. 52
3. 74
4. 58

Q. $Ifa+b+c=m\text{and}{a}^2+b^2+c^2=n,\text{then}(ab+bc+ca)is$

1. $\frac{m^2-n}{2}$
2. $\frac{n^2-m}{2}$
3. $\frac{n^2-m}{4}$
4. $\frac{m^2-n}{4}$

Q. Question 3(iii)
Simplify:
$(t+s^2)(t^2-s)$

Q. If $a+b+c=9and2(ab+bc+ca)=46,then{a}^2+b^2+c^2$ is :

1. 32
2. 58
3. 53
4. 35

Q.

What is the product of the rational expressions below?

$\frac{4x}{x+6}·\frac{x-8}{x-6}$

1. $\frac{4x^2-32}{x^2}$

2. $\frac{4x^2-32}{x^2-12}$

3. $\frac{4x^2-32x}{x^2-36}$

4. $\frac{4x^2-8}{x^2-36}$

Q. $Ifa+b+c=10and{a}^2+b^2+c^2=38,then(ab+bc+ca)$ is :

1. 62
2. 31
3. 64
4. 32

Q. Simplify: $(m^2-n^{2}m{)}^2+2m^3{n}^2$

1. $m^4+m^2{n}^4+4m^3{n}^2$
2. $m^4+m^4{n}^2+4m^3{n}^2$
3. $m^2+m^4{n}^2$
4. $m^4+m^2{n}^4$