Algebraic Expressions Test

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Algebraic Expressions Test - 11

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Weekly Quiz Competition

Question 1
1 / -0

By how much is x$$^4$$ + 4x$$^2$$y$$^2$$ + y$$^4$$ more than x$$^4$$ - 8x$$^2$$y$$^2$$ + y$$^4$$ ?

A
-12x$$^2$$y$$^2$$

B
12x$$^2$$y$$^2$$

C
2x$$^4$$ + 2y$$^4$$

D
None of these

Solution

(x⁴ + 4x²y² + y⁴) - (x⁴ - 8x²y² + y⁴)
= x⁴ + 4x²y² + y⁴ - x⁴ + 8x²y² - y⁴= 12 x²y²
Question 2
1 / -0

If we add two monomials, what will be the result?

A
Monomial

B
Binomial

C
Polynomial

D
Either $$A$$ or $$B$$

Solution

If two monomials are added we will get a result which is addition of two terms.
So in most of the cases, the result will be a binomial but in other cases, when both terms differ by coefficients, their addition will give another monomial.
For eg. $$3x$$, $$4y$$ when added, gives $$3x+4y$$.
However, $$5x^2+7x^2$$ when added, gives $$5x^2+7x^2=12x^2$$.
Question 3
1 / -0

By how much is a$$^4$$ - 4a$$^2$$b$$^2$$ + b$$^4$$ less than a$$^4$$ + 8a$$^2$$b$$^2$$ + b$$^4$$ ?

A
12a$$^2$$b$$^2$$

B
-12ab

C
12ab

D
-12a$$^2$$b$$^2$$

Solution

(a⁴ + 8a²b² + b⁴) - (a⁴ - 4a²b² + b⁴)
= a⁴ + 8a²b² + b⁴ - a⁴ + 4a²b² - b⁴
= 8a²b² + 4a²b^2
=12a²b²
Question 4
1 / -0

$$\displaystyle 5a-\{ { 3a-(4-a)-4\} }$$ is equal to

A
$$\displaystyle 3a+8$$

B
$$\displaystyle a-8$$

C
$$\displaystyle a+8$$

D
$$\displaystyle 3a-8$$

Solution

Given, $$\displaystyle 5a-\{ { 3a-(4-a)-4\} }$$
$$=\displaystyle 5a-\left\{ 3a-4+a-4 \right\} $$
$$=\displaystyle 5a-\left\{ 4a-8 \right\} $$
$$\displaystyle= 5a-4a+8$$
$$=\displaystyle a+8$$, which is simplified form.
Question 5
1 / -0

$$5x^{3} + 5x^{2} + 4x + 3 + 4x^{2} + 5x =$$

A
$$9x^{3} + 4x^{2} + 4x + 5$$

B
$$5x^{3} + 5x^{2} + 9x + 4$$

C
$$5x^{3} + 9x^{2} + 9x + 3$$

D
None of the above

Solution

$$5x^{3} + 5x^{2} + 4x + 3 + 4x^{2} + 5x$$
$$=5x^{3} + 9x^{2} + 9x + 3$$
Question 6
1 / -0

How many terms are there in the algebraic expression $$7x^3+2xy+z-7y$$?

A
$$3$$

B
$$4$$

C
$$5$$

D
$$6$$

Solution

There are 4 terms. The terms are $$7x^3, 2xy, z, 7y$$
Question 7
1 / -0

If we add $$3+7x$$ and $$11x$$ , what will be the result?

A
monomial

B
binominal

C
trinimial

D
can"t be determined

Solution

$$(3+7x)+11x=3+18x$$ is a binomial.
Question 8
1 / -0

If we add $$7x$$ and $$5y^2+z$$ , what will be the result?

A
binomial

B
trinomial

C
polynimial

D
can"t be determind

Solution

$$(7x)+(5y^2+z) =7x+5y^2+z$$ is a trinomial
Question 9
1 / -0

Find an equivalent simplified expression for $$\displaystyle 2\left( 4x+7 \right) -3\left( 2x-4 \right) $$.

A
$$\displaystyle x+2$$

B
$$\displaystyle 2x+2$$

C
$$\displaystyle 2x+26$$

D
$$\displaystyle 3x+10$$

E
$$\displaystyle 3x+11$$

Solution

The value of $$2(4x+7)-3(2x-4)$$
$$\Rightarrow 8x+14-6x+12$$
$$\Rightarrow 2x+26$$
Question 10
1 / -0

Simplify the expression: $$\displaystyle { t }^{ 2 }-59t+54-82{ t }^{ 2 }+60t$$

A
$$\displaystyle -26{ t }^{ 2 }$$

B
$$\displaystyle -26{ t }^{ 6 }$$

C
$$\displaystyle -81{ t }^{ 4 }+{ t }^{ 2 }+54$$

D
$$\displaystyle -81{ t }^{ 2 }+{ t }+54$$

Solution

$$t^2-59t+45-82t^2+60t$$
$$\Rightarrow t^2-82t^2+60t-59t+54$$
$$\Rightarrow -81t^2+t+54$$

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Re-Attempt Weekly Quiz Competition

Algebraic Expressions Test - 11

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Algebraic Expressions Test - 11

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Question 1

-12x$$^2$$y$$^2$$

12x$$^2$$y$$^2$$

2x$$^4$$ + 2y$$^4$$

None of these

Solution

Question 2

Monomial

Binomial

Polynomial

Either $$A$$ or $$B$$

Solution

Question 3

12a$$^2$$b$$^2$$

-12ab

12ab

-12a$$^2$$b$$^2$$

Solution

Question 4

$$\displaystyle 3a+8$$

$$\displaystyle a-8$$

$$\displaystyle a+8$$

$$\displaystyle 3a-8$$

Solution

Question 5

$$9x^{3} + 4x^{2} + 4x + 5$$

$$5x^{3} + 5x^{2} + 9x + 4$$

$$5x^{3} + 9x^{2} + 9x + 3$$

None of the above

Solution

Question 6

$$3$$

$$4$$

$$5$$

$$6$$

Solution

Question 7

monomial

binominal

trinimial

can"t be determined

Solution

Question 8

binomial

trinomial

polynimial

can"t be determind

Solution

Question 9

$$\displaystyle x+2$$

$$\displaystyle 2x+2$$

$$\displaystyle 2x+26$$

$$\displaystyle 3x+10$$

$$\displaystyle 3x+11$$

Solution

Question 10

$$\displaystyle -26{ t }^{ 2 }$$

$$\displaystyle -26{ t }^{ 6 }$$

$$\displaystyle -81{ t }^{ 4 }+{ t }^{ 2 }+54$$

$$\displaystyle -81{ t }^{ 2 }+{ t }+54$$

Solution

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