Answer :
To find the expression for the area of a rectangle, we use the formula for the area, which is:
[tex]\[ \text{Area} = \text{Length} \times \text{Width} \][/tex]
Given the length of the rectangle is \((x - 8)\) units and the width is \((x + 11)\) units, we can set up the equation for the area as follows:
[tex]\[ \text{Area} = (x - 8) \times (x + 11) \][/tex]
To find the resulting expression for the area, we need to expand the product of these two binomials. We can use the distributive property (also known as the FOIL method for binomials):
[tex]\[ (x - 8)(x + 11) = x(x) + x(11) - 8(x) - 8(11) \][/tex]
Now, let's perform the multiplication step-by-step:
1. Multiply the first terms: \(x \times x = x^2\)
2. Multiply the outer terms: \(x \times 11 = 11x\)
3. Multiply the inner terms: \(-8 \times x = -8x\)
4. Multiply the last terms: \(-8 \times 11 = -88\)
After multiplying, we combine these terms:
[tex]\[ x^2 + 11x - 8x - 88 \][/tex]
Combine the like terms (\(11x\) and \(-8x\)):
[tex]\[ x^2 + 3x - 88 \][/tex]
Therefore, the expression that represents the area of the rectangle is:
[tex]\[ x^2 + 3x - 88 \][/tex]
So, the correct answer is:
C. [tex]\(x^2 + 3x - 88\)[/tex]
[tex]\[ \text{Area} = \text{Length} \times \text{Width} \][/tex]
Given the length of the rectangle is \((x - 8)\) units and the width is \((x + 11)\) units, we can set up the equation for the area as follows:
[tex]\[ \text{Area} = (x - 8) \times (x + 11) \][/tex]
To find the resulting expression for the area, we need to expand the product of these two binomials. We can use the distributive property (also known as the FOIL method for binomials):
[tex]\[ (x - 8)(x + 11) = x(x) + x(11) - 8(x) - 8(11) \][/tex]
Now, let's perform the multiplication step-by-step:
1. Multiply the first terms: \(x \times x = x^2\)
2. Multiply the outer terms: \(x \times 11 = 11x\)
3. Multiply the inner terms: \(-8 \times x = -8x\)
4. Multiply the last terms: \(-8 \times 11 = -88\)
After multiplying, we combine these terms:
[tex]\[ x^2 + 11x - 8x - 88 \][/tex]
Combine the like terms (\(11x\) and \(-8x\)):
[tex]\[ x^2 + 3x - 88 \][/tex]
Therefore, the expression that represents the area of the rectangle is:
[tex]\[ x^2 + 3x - 88 \][/tex]
So, the correct answer is:
C. [tex]\(x^2 + 3x - 88\)[/tex]
