Question
In front of a school are several gardens in rectangular raised beds. For the area of the rectangular area given, use factoring to find the possible dimensions. Could the garden be square?
x2 – 4y2
- x – 2y, Square
- x + 2y by x - 2y, Rectangle
- x + 2y, Square
- x + 3y by x – 3y, Rectangle
Hint:
Algebraic expressions are those that are modelled utilising unknowable constants, coefficients, and variables. A constant has a fixed value, whereas a variable can have any value since it is not fixed. An algebraic expression with three terms is called a trinomial. Here we have given that in front of the school are several gardens in rectangular raised beds. The area is x2 – 4y2, using factorisation, we have to find the possible dimensions.
The correct answer is: x + 2y by x - 2y, Rectangle
Now we know that an algebraic expression known as a trinomial has three non-zero terms and more than one variable. An example of a binomial is a polynomial having two terms. It is in the form of ax2+bx, for example 5x4 - 4x
We have also been given the trinomial here. The expression is: x2 – 4y2
Now we can see that 4 is the square of 2, So we can re-write the given expression as:
x2 – 4y2 = (x)2 - (2y)2
Now we can use the formula: a2-b2=(a+b)(a-b), we get:
x2 – 4y2 = (x)2 - (2y)2 = (x - 2y)(x + 2y)
So, the side lengths are x + 2y and x – 2y. So, it has unequal length and width. Then it is a rectangle.
Here we used the concept of algebriac equations, trinomials and squares to factories the given expression. An expression with variables, constants, and algebraic operations is known as an algebraic expression (like subtraction, addition, multiplication, etc.). Terms comprise expressions. So, the side lengths are x + 2y and x – 2y. So, it has unequal length and width. Then it is a rectangle.
Related Questions to study
In front of the school are several gardens in rectangular raised beds. For the area of the rectangular area given, use factoring to find the possible dimensions. Could the garden be square?
x2 + 32x + 256
Here we used the concept of algebriac equations, trinomials and squares to factories the given expression. An expression with variables, constants, and algebraic operations is known as an algebraic expression (like subtraction, addition, multiplication, etc.). Terms comprise expressions. So the side length is (x + 16) and all the sides are equal in length. So, it is a square.
In front of the school are several gardens in rectangular raised beds. For the area of the rectangular area given, use factoring to find the possible dimensions. Could the garden be square?
x2 + 32x + 256
Here we used the concept of algebriac equations, trinomials and squares to factories the given expression. An expression with variables, constants, and algebraic operations is known as an algebraic expression (like subtraction, addition, multiplication, etc.). Terms comprise expressions. So the side length is (x + 16) and all the sides are equal in length. So, it is a square.
Two pieces of fabric are being used for clothing designs for a fashion show at school. Expressions for the areas of the rectangular piece are shown.
Factor the expressions for the areas completely.
a²+2ab+b² = (a+b)².
Two pieces of fabric are being used for clothing designs for a fashion show at school. Expressions for the areas of the rectangular piece are shown.
Factor the expressions for the areas completely.
a²+2ab+b² = (a+b)².
Given the area of the square, factor to find the side length.
A = 144x2 – 24x + 1
Given the area of the square, factor to find the side length.
A = 144x2 – 24x + 1
Factor 64x2y2 – 144z2
Factor 64x2y2 – 144z2
Factors -3x3 + 18x2 – 27x
Factors -3x3 + 18x2 – 27x
Factor 121x2 + 110x + 25
Factor 121x2 + 110x + 25
Factor 49x3 – 16xy2
Factor 49x3 – 16xy2
Factor 7x3y – 63xy3
Factor 7x3y – 63xy3
A furniture company created an L-shaped table by removing part of a square table.
Write an expression that represents the area of the L-shaped table.
a²-b² = (a-b)(a+b).
A furniture company created an L-shaped table by removing part of a square table.
Write an expression that represents the area of the L-shaped table.
a²-b² = (a-b)(a+b).
Select all polynomials that factor into a product into two binomials.
a) 25m2 – 9n2
b) 25m2 – 30mn + 9n2
c) 25m2 – 30mn – 9n2
d) 25m2 + 30mn + 9n2
e) 25m2 + 9n2
Factorisation is breaking down of a polynomial into polynomials of lesser degrees.
Select all polynomials that factor into a product into two binomials.
a) 25m2 – 9n2
b) 25m2 – 30mn + 9n2
c) 25m2 – 30mn – 9n2
d) 25m2 + 30mn + 9n2
e) 25m2 + 9n2
Factorisation is breaking down of a polynomial into polynomials of lesser degrees.
