Question

squares
squaring numbers, polynomials and rational expressions is something you have done many times in algebra. we use the word “squaring” to mean multiplying a number or expression by itself, because this is what we do to find the areas of squares.
find the area of each shaded square.
write an expression for the area of each square.
5 a=
43 a=
1.2 a=
1/3 a=
2/3 a=
x + 3 a=
m a=
2x - 1 a=
6y/z a=

Explanation:

Step1: Recall the area formula for a square

The area formula of a square is $A = s^{2}$, where $s$ is the side - length of the square.

Step2: Calculate the area of the numerical - side - length squares

For a square with side - length $s = 5$, $A=5^{2}=25$; for $s = 43$, $A = 43^{2}=1849$; for $s = 1.2$, $A=1.2^{2}=1.44$; for $s=\frac{1}{3}$, $A = (\frac{1}{3})^{2}=\frac{1}{9}$; for $s=\frac{2}{3}$, $A=(\frac{2}{3})^{2}=\frac{4}{9}$.

Step3: Expand the algebraic - side - length squares

For a square with side - length $s=x + 3$, use the formula $(a + b)^2=a^{2}+2ab + b^{2}$, so $A=(x + 3)^2=x^{2}+6x + 9$. For $s = m$, $A=m^{2}$. For $s = 2x-1$, use the formula $(a - b)^2=a^{2}-2ab + b^{2}$, so $A=(2x - 1)^2=4x^{2}-4x + 1$. For $s=\frac{6y}{z}$, $A=(\frac{6y}{z})^{2}=\frac{36y^{2}}{z^{2}}$.

Answer:

1. For the square with side - length 5: $A = 25$
2. For the square with side - length 43: $A = 1849$
3. For the square with side - length 1.2: $A = 1.44$
4. For the square with side - length $\frac{1}{3}$: $A=\frac{1}{9}$
5. For the square with side - length $\frac{2}{3}$: $A=\frac{4}{9}$
6. For the square with side - length $x + 3$: $A=(x + 3)^2=x^{2}+6x + 9$
7. For the square with side - length $m$: $A = m^{2}$
8. For the square with side - length $2x-1$: $A=(2x - 1)^2=4x^{2}-4x + 1$
9. For the square with side - length $\frac{6y}{z}$: $A=\frac{36y^{2}}{z^{2}}$