Distributivity

Q.

Using identities, evaluate $78x82$

Q. Find the value of $\frac{2}{5}\times \frac{10}{9}-\frac{8}{5}+\frac{10}{9}\times \frac{7}{5}$.

Q. Name the property under multiplication used in each of the following.
$-\frac{13}{17}\times \frac{-2}{7}=\frac{-2}{7}\times \frac{-13}{17}$

Q. A square has a larger area than any other rhombus having the same side length. State true or false.

1. True
2. False

Q. Find the value of $\frac{2}{5}\times \frac{10}{9}-\frac{8}{5}+\frac{10}{9}\times \frac{7}{5}$.

Q. The base of a parallelogram is' b' units. If its height is 14 more than its base, find the area of the parallelogram.

1. ($b^2$ - 14b) sq. units
2. ($b^2$ + 14b) sq. units
3. ($b^2$) sq.units
4. (b +14) sq.units

Q. Name the property used in the following:
$\frac{1}{2}+\frac{3}{5}=\frac{3}{5}+\frac{1}{2}$

Q. 3a ( $8y^2$ - $6z^2$) = $3a\times 8y^2$ - $3a\times 6z^2$.
The above applies the ___________ property to simplify an algebraic expression.

1. Associative
2. Commutative
3. Distributive
4. None of the above.

Q. What should be subtracted from $x^2-4xy-y^2$ to get $1$?

1. ${-x}^2-4xy+y^2$
2. ${-x}^2+4xy+y^2+1$
3. $x^2-4xy-y^2-1$
4. ${-x}^2+4xy+y^2-1$

Q. Expansion of $-8(3a+5b)$ yields

1. $-24a-40b$
2. $-22a+80b$
3. $20a-30b$
4. $-24a-41b$

Q. Find and correct errors of the following mathematical expressions:
$(y-3{)}^2=y^2-9$

Q. $\frac{4}{5}\times \frac{11}{2}-\frac{9}{10}\times \frac{11}{2}=\frac{11}{2}\times$().

Q. 10. find the value of a and b , 3-1 divided by 3+1=a+b3

Q. 25 x a5 x 10 + 5 raise to the power 3 x a raise to the power-3.

Q. If the sum of two integers is $12$ and their difference is $4$ then the greater number is ________.

1. $7$
2. $6$
3. $8$
4. $9$

Q. Expansion of $-8(3a+5b)$ yields

1. $-24a-40b$
2. $-22a+80b$
3. $20a-30b$
4. $-24a-41b$

Q. $\frac{4}{5}\times \frac{11}{2}-\frac{9}{10}\times \frac{11}{2}=\frac{11}{2}\times$().

Q. Factories the following algebraic expression by regrouping
$p^2{y}^2+(p{y}^2+1)y+p$

Q. The final value of the expression $\sqrt{225}+\sqrt{100}$ is

1. 20
2. 35
3. 30
4. 25

Q. The value of ${11}^2-5^2$ is _____.

1. 100
2. 96
3. 80
4. 70

Q. The final value of the expression $\sqrt{225}+\sqrt{100}$ is

1. 20
2. 35
3. 30
4. 25