Expansion of (a ± b ± c)²

Q.

What is formula for $x^2+y^2$?

Q.

Simplify:
$\frac{3^{-5}\times {10}^{-5}\times 125}{5^{-7}\times 6^{-5}}$

Q.

Simplify ${\left(2x-5y\right)}^3-{\left(2x+5y\right)}^3$

Q.

If the arithmetic, geometric and harmonic means between two distinct positive real numbers be $A,G$ and $H$ respectively, then the relation between them is:

1. $A>G>H$

2. $A>G<H$

3. $H>G>A$

4. $G>A>H$

Q.

The total number of terms in the expansion of ${(x+y)}^{100}+{(x–y)}^{100}$after simplification is

1. $51$

2. $202$

3. $100$

4. $50$

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

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

Q.

The value of ${\sin }^{2}5°+{\sin }^{2}10°+{\sin }^{2}15°+......+{\sin }^{2}85°+{\sin }^{2}90°$ is equal to

1. $7$

2. $8$

3. $9$

4. $9\frac{1}{2}$

Q. Question 4
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) ${[\frac{1}{4}a-\frac{1}{2}b+1]}^2$

Q. Question 2
Evaluate the following products without multiplying directly:
(i) 100 $\times$ 107
(ii) 95 $\times$ 96
(iii) 104 $\times$ 96

Q.

Evaluate the following using suitable identities:
(i)$(99{)}^3$
(ii) $(102{)}^3$
(iii) $(998{)}^3$

Q. Question 30
if $a+b+c=9$ and $ab+bc+ca=26$, find $a^2+b^2+c^2$.

Q.

If $p=2^a\times 3^b\times 5^c$ and $a>b>c$ are natural numbers, then what is the unit digit of $p$?

1. 1

2. 0

3. 2

4. 3

Q.

Use suitable identities to find the following product: (3x + 4) (3x – 5)

Q.

Factorise: $2x^3-3x^2-17x+30$

Q.

Which of the following equation/s is/are correct?

$i\left)\right(a+b+c{)}^2=a^2+b^2+c^2-2(ab+bc+ca)$
$ii\left)\right(a+b{)}^3=a^3+b^3+3ab(a-b)$
$iii\left)\right(a-b{)}^3=a^3-b^3-3ab(a+b)$
$iv)a^2-b^2=(a+b\left)\right(a-b)$

1. (iv) and (iii)

2. (i) and (iv)

3. (iv) only

4. (ii), (iii) and (iv)

Q. If x = 9-4$\sqrt{5}$, find the value of $x^2+\frac{1}{x^2}$

Q.

Question 1(f)
Find the following product:
$(-12)\times (-11)\times \left(10\right)$

Q. Simplify: $625\times (-35)+(-625)\times 65$

Q. Simplify $\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}$

Q.

By which rational number would you multiply $\frac{5}{12}$ , to get the product 1?
[1 MARK]

Q.

Question 3 (ix)
Find
0.5 $\times$ 10

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

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

Q.

Question 1 (h)

Write all the factors of the given number:
23

Q.

Expand the following, using suitable identities:

${(2x-y+z)}^2$ [3 MARKS]

Q.

If one of the two factors of an expression which is the difference of two cubes is ($x^4$ + $x^2$y + $y^2$), then the other factor would be -

Q. If $X=\sqrt{3}-\sqrt{2}$ then find $X^2+1/X^2$

Q.

Question 54

Fill in the blanks to make the statement true.

___ $\times$ (-1) = 47

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

1. $4x^2+4y^2+z^2+8xy-4yz-4xz$
2. $4x^2+4y^2+4z^2+8xy-4yz-4xz$
3. $4x^2+4y^2+z^2+8xy-8yz-4xz$
4. $4x^2+4y^2+z^2+8xy-4yz-8xz$

Q. If $a+b+c=m$ and $a^2+b^2+c^2=n$,
then $2(ab+bc+ca)$ is _______.

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

Q.

How do you simplify ${\left(\frac{2}{3}\right)}^{-1}$?