Distributive Property of Multiplication

Q.

${\left(x+iy\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}=a+ib$, then $\left(\frac{x}{a}\right)+\left(\frac{y}{b}\right)$ is equal to

1. $4\left(a^2+b^2\right)$

2. $4\left(a^2-b^2\right)$

3. $4\left(b^2-a^2\right)$

4. None of these.

Q.

Expand ${(2a-3b)}^3$.

Q. Find the product using distributive property.
625 x 279 - 625 x 79

1. 
   125000
2. 
   120000
3. 
   130000
4. 
   135000

Q. Question 83 (viii)

Multiply the following:
$x^2{y}^2{z}^2$ and (xy - yz + zx)

Q.

Question 83 (vi)

Multiply the following :

abc, (bc + ca)

Q.

Find the product by a suitable rearrangement:
$4\times 166\times 25$

Q.

Question 4(a)
Simplify : 3x (4x-5) +3 and find values for (i) x=3 (ii) x= $\frac{1}{2}$

Q.

Find the product by applying suitable properties.

$238\times 103$

Q.

Question 83 (vii)

Multiply the following:

7pqr, (p - q + r)

Q. Question 1(iv)
Carry out the multiplication of the expressions in each of the following pairs:
$a^2-9,4a$

Q.

$\text{Using an identity, evaluate}166\times 94.$

1. 15604

2. 14551

3. 14562

4. 13552

Q.

Question 1(i)
Carry out the multiplication of the expressions in each of the following pairs:
4p, q+r

Q. Find the value of 407$\times$ 393 using a suitable identity.

Q.

___ $\times \left(-1\right)=-35$

Q.

Question 83 (iii)

Multiply the following :

$15x{y}^2,17y{z}^2$

Q.

$\text{Using an identity, evaluate}166\times 94.$

1. 15604

2. 14551

3. 14562

4. 13552

Q.

Question 1(v)
Carry out the multiplication of the expressions in each of the following pairs:
pq+qr+rp, 0

Q. If x + y = 12 and xy = 14, find the value of (x² + y²).

Q. Question 36

In the question given below, fill in the blanks to make the statement true:

$a(b+c)=a\times$ ___ $+a\times$ ___

Q.

$4.1xy(1.1x-y)$

Q.

Which of the following correctly explains distributive law?

1. $a\times (b+c)=b\times a+a\times c$

2. $b\times (a+c)=b\times a+b\times c$

3. $(a+c)\times b=a\times b+c\times b$

4. All of these

Q.

The quotient when $6ab-b^2+12ac-2bc$ is divided by $(6a-b)$ is ___

Q. Simplify $8(3h-4)+5(h-2)$.

1. $24h-37$
2. $36-4h$
3. $29h-42$
4. $38+42h$

Q.

Find the squares of the following algebraic expressions

(i) 2x + 3y

(ii) x + 2

(iii) 2x + 1

Q.

Find and correct the errors in the statement: x(3x + 2) = 3x² + 2

Q. Find product of following pairs of monomials
(i) $4,7p$
(ii) $-4p,7p$
(iii) $-4p,7pq$
(iv) $4p^3,-3p$
(v) $4p,0$

Q. Simplification of $\frac{(p+a)}{5}=3p$ yields

1. $12\times \frac{p}{a}=5$
2. $a=\frac{p}{5}$
3. $a=14p$
4. $a=15p$

Q. Find the product:
(3p² + q²) × (2p² − 3q²)

Q. The value of $(a+b)(a+c)(b+c)$, where $a=1$, $b=2$ and $c=3$ will be .

1. 46
2. 60
3. 50

Q.

25a² − 4b² + 28bc − 49c²