Expansion of (a+b)^3

Q. If a + 2b = 5, then find the value of $a^3+8b^3+30ab$.

1. 100
2. 150
3. 75
4. 125

Q. The sum of two numbers is 9 and their product is 20. Find the sum of their cubes.

1. 189
2. 1269
3. 190
4. 79

Q.

The value of the expression $\frac{10\times 10\times 10+5\times 5\times 5}{10\times 10-10\times 5+5\times 5}$ is :

1. $15$
2. $10$
3. $5$
4. $20$

Q. $\text{If}(a^3+b^3)=243\text{and}(a+b)=9,\text{then the value of}(a^2-ab+b^2)\text{is}$

1. 9
2. 27
3. 18
4. 36

Q. Find the cube of 5a+3b .

1. $125a^3-225a^{2}b-135a{b}^2-27b^3$
2. $125a^3+27b^3+225a^{2}b+135a{b}^2$
3. $125a^3+125a^{2}b+135a{b}^2-27b^3$
4. $125a^3-225a^{2}b-135a{b}^2-27b^3$

Q.

${\text{a}}^2{\text{-b}}^2$ is equal to

1. $({\text{a-b)}}^2$

2. $(\text{a-b)(a-b)}$

3. $(\text{a+b)(a-b)}$

4. $(\text{a+b)(a+b)}$

Q.

Fill in the blank

$13+\_\_\_=0$

Q. If $a+b+c=0$, then the value of $(a+b-c{)}^3+(b+c-a{)}^3+(c+a-b{)}^3$ is:

1. $24abc$
2. $8(a^3+b^3+c^3)$
3. $a^3+b^3+c^3$
4. $-24abc$

Q. Evaluate 7³ + 3³ + (-10)³ .

1. -630
2. 630
3. 360
4. -360

Q. Expand: (i) $(7x+8y{)}^3$ (ii) $101{)}^3$

Q. Expand $(a-b-c{)}^2$ using expansion formula $(a+b+c{)}^2$.

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

Q. Expand: $(3x+4y{)}^3$

1. $27x^3-108x^{2}y-144x{y}^2-64y^3$
2. $27x^3+108x^{2}y+144x{y}^2+64y^3$
3. $9x^3+36x^{2}y+48x{y}^2+16y^3$
4. $27x^2+108x{y}^2+144x^{2}y+64y^2$

Q. Evaluate (38)³ + (-26)³ + (-12)³.

1. 36578
2. 35568
3. 31058
4. 36549

Q. Evaluate (13)³ + (-8)³ + (-5)^{3 .}

1. 1650
2. 1500
3. 1200
4. 1560

Q.

Simplify the following :

$\left(i\right){(5a-8b)}^2-{(5a+8b)}^2$

$\left(ii\right){(2a+3b)}^2-\left(\right(2a+3b\left)\right(2a-3b\left)\right)$ [4 MARKS]

Q.

Simplify: $(x-y)(x+y)(x^2+y^2)(x^4+y^4)$

1. $x^8-y^8$
2. $x^4-y^4$
3. $x^8-y^8$
4. $x^4+y^2$

Q. Find the coefficient of y in the product of (y + 4)(y + 4)(y + 4).

1. 12
2. 24
3. 36
4. 48

Q. If $a+\frac{1}{a}$ = 4, the value of $a^3+\frac{1}{a^3}$ is equal to .

1. $42$
2. $56$
3. $62$
4. $52$

Q. Find the cube of 3x - 2y - 4z

1. $27x^3-54x^{2}y+36x{y}^2-8y^3-108x^{2}z+144xyz-48y^{2}z+144x{z}^2-96y{z}^2-64z^3$
2. $81x^3-54x^{2}y+36x{y}^2-8y^3-108x^{2}z+144xyz-48y^{2}z+169x{z}^2-96y{z}^2-27z^3$
3. $81x^3+54x^{2}y+36x{y}^2-8y^3-108x^{2}z+27xyz-48y^{2}z+169x{z}^2-96y{z}^2-27z^3$
4. $27x^3+54x^{2}y+36x{y}^2+8y^3+108x^{2}z+144xyz-48y^{2}z+144x{z}^2-96y{z}^2-64z^3$

Q. $(1-2a{)}^2=4(1-a{)}^2$

Q. Find the cube of $2a+\frac{1}{2a}$ ( $a\ne$0) .

1. $4a^3+\frac{1}{4a^3}+4a+\frac{8}{2a}$
2. $8a^3-\frac{1}{8a^3}-6a-\frac{3}{2a}$
3. $8a^3+\frac{1}{8a^3}+6a+\frac{3}{2a}$
4. $16a^3-\frac{1}{8a^3}+6a-\frac{8}{2a}$

Q. The expansion of ($x-6$)($x+5$)($x-4$) is _____.

1. $x^3+18x^2+26x+24$
2. $x^3+9x^2+26x+120$
3. $x^3+9x^2+26x+24$
4. $x^3-5x^2-26x+120$

Q.

Calculate the value of the expression using suitable identities $4\times 2\times (3^2+1^2)$

1. 79

2. 80

3. 78

4. 81

Q. If $a^2+\frac{1}{a^2}=34$, then the value of $a^3+\frac{1}{a^3}$ is equal to.

1. $\pm 234$
2. $98$
3. $\pm 198$
4. $\pm 99$

Q. If ${\left(a+\frac{1}{a}\right)}^2$ = 3 and a$\ne 0$; then the value of $a^3+\frac{1}{a^3}$ is

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

Q. If $a+\frac{1}{a}$ = 4, the value of $a^3+\frac{1}{a^3}$ is equal to .

1. $42$
2. $56$
3. $62$
4. $52$