Simplifying Polynomial Expressions: Difficult Problems with Solutions

By Catalin David
Problem 1
Which of these is a monomial,
$-\dfrac{6}{x^{-5}}$ or $\dfrac{6}{-x^{5}}$?
Problem 2
What is $-2x^{4}+5x^{4}$ ?
Problem 3
2x2y - 17x2y=
Problem 4
$-8xy^{3}-12xy^{3}=$
Problem 5
$-5x^{6}+(-4x^{6})=$
Problem 6
$14x^{4}-(-9x^{4})=$
Problem 7
$3\cdot(-2x^{4})-5\cdot(-4x^{4})=$
Problem 8
$4x^{2}y^{3}\cdot3xy=$
Problem 9
$-3x^{4}y^{7}\cdot(-4)x^{5}y^{6}=$
Problem 10
Area of rectangle ABCD is:



Problem 11
$12x^{4}y^{7}\div4x^{2}y^{4}=$
Problem 12
$-16x^{14}y^{8}\div(-8)x^{7}y^{5}$
Problem 13
$42x^{10}y^{5}\div(-6)x^{7}y^{5}=$
Problem 14
$(2x^{4}y^{3})^{5}=$
Problem 15
$(-5x^{2}y^{4})^{2}=$
Problem 16
The area of square ABCD is:


Problem 17
The volume of a cube with sides $3x^{4}$ is:


Problem 18
$[AB]=3x^{2}+1$
$[BC]=5x^{2}-4$
Find [AC]=?


Problem 19
$[AB]=3x^{2}+1$
$[AC]=7x^{2}-3$
Find [BC]= ?


Problem 20
Calculate the perimeter of the triangle ABC.


Problem 21
The perimeter of square ABCD is:


Problem 22
Perimeter of rectangle ABCD is:


Problem 23
Let the polynomials be:
$P_{1}(x)=3x^{2}-7x+5$
$P_{2}(x)=-5x^{2}-4x+2$
$P_{1}(x)+P_{2}(x)=$
Problem 24
Given two polynomials:
$P_{1}(x)=-4x^{3}+2x^{2}+3$
$P_{2}(x)=-2x^{3}+7x^{2}-6$
Calculate $P_{1}(x)-P_{2}(x)=$
Problem 25
Given two polynomials:
$P_{1}(x)=3x^{3}-2x^{2}-4x +5$
$P_{2}(x)=-2x^{3}+3x^{2}-2x +1$
Calculate:
$3P_{1}(x)-2P_{2}(x)=$
Problem 26
$5x\cdot(2x^{2}-3x+4)-3x^{2}\cdot(-6x^{3}+4x^{2}+2x-1)=$
Problem 27
Area of rectangle ABCD is:


Problem 28
The volume of the parallelepiped is:


Problem 29
$(3x^{2}+4)^{2}=$
Problem 30
$(2x^{2}-1)^{2}=$
Problem 31
$(x^{2}+6)\cdot(x^{2}-6)=$
Problem 32
(x3 + 1)⋅(x3 - 1)=
Problem 33
(9x2 + 4)⋅(9x2 - 4) =
Problem 34
(2x - 3)(4x + 1) + (3x + 5)(x - 2) =
Problem 35
(5x - 2)(3x + 4) - (2x + 7)(x + 3) =
Problem 36
(x - 3)2 - (x + 4)2=
Problem 37
(2x + 5)2 - (3x - 4)2=
Problem 38
(2x + 1)2 + (x - 2)2 =
Problem 39
(x - 1)(x + 1) - (x - 3)(x + 3)=
Problem 40
(2x - 3)(2x + 3) - (3x - 5)(3x + 5) =
Problem 41
(4x - 7)(4x + 7) + (2x - 9)(2x + 9) =
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