Test: Algebraic Expressions And Identities- 2 - Class 8 MCQ

An algebraic expression that contains only one term is called a:

A monomial is a single term expression in algebra.

• For example, 2x is a monomial.

The expression containing two terms is called a binomial. In this case:

• 5x is the first term.
• 6y is the second term.

This makes the entire expression a binomial.

Given, 7xy + 5yz – 3zx, 4yz + 9zx – 4y and –3xz + 5x – 2xy.
If we add the three expressions, then we need to combine the like terms together.
(7xy – 2xy) + (5yz + 4yz) – 3zx + 9zx – 3xz – 4y + 5x
= 5xy + 9yz + 3zx + 5x – 4y

(12a – 9ab + 5b – 3) – (4a – 7ab + 3b + 12)
= 12a – 9ab + 5b – 3 – 4a + 7ab -3b-12
= (12 – 4)a – (9 – 7)ab + (5 – 3)b – 3 – 12
= 8a – 2ab + 2b – 15

(5x)* (-4xyz)

= 5 * x * (-4) * x * y * z

= -20x¹⁺¹yz

= -20x²yz

The product of 3xy²z and 4x is:
⇒ (3xy²z) (4x)
⇒ 3.x.y².z.4.x
⇒ 12x²y²z

- When multiplying any expression by zero, the result is always zero.
- Thus, the product of pq+qr+rp and ‘zero’ is 0.

Answer: D: 0

The expression 564xy is a monomial because it consists of a single term, which includes variables and coefficients combined through multiplication.

• Each variable (x and y) contributes to the same term.
• There are no addition or subtraction operations involved.
• This fits the definition of a monomial.

The area of a square is calculated by squaring the length of its side. Given the side length is 5x²y, the area is:

• (5x²y)² = 25x⁴y².

Thus, the correct answer is option B.

The area of a rectangle can be calculated using the formula:

• Area of rectangle = Length × Breadth

For this specific rectangle, the lengths are:

• Length = 3x²y
• Breadth = 5xy²

Substituting these values into the formula gives:

• Area = (3x²y) × (5xy²)

Now, let's perform the multiplication:

• Area = 15x³y³ m²

Thus, the area of the rectangle is 15x³y³ m².

To simplify (x + y + z)(x + y - z), notice that the expression is of the form (A + z)(A - z) where A = (x + y). This product equals A² - z².

Now, compute A²

A² = (x + y)² = x² + 2xy + y²

Subtract z²: x² + 2xy + y² - z²

This matches option (a).

Answer: a) x² + y² – z² + 2xy

To simplify the expression x²(x - 3y²) - xy(y² - 2xy) - x(y³ - 5x²), follow these steps:

1. Expand each term separately:
   • x²(x - 3y²) = x³ - 3x²y²
   • -xy(y² - 2xy) = -xy³ + 2x²y²
   • -x(y³ - 5x²) = -xy³ + 5x³
2. Combine all expanded terms:

   x³ - 3x²y² - xy³ + 2x²y² - xy³ + 5x³

3. Combine like terms:
   • x³ + 5x³ = 6x³
   • -3x²y² + 2x²y² = -x²y²
   • -xy³ - xy³ = -2xy³

The simplified expression is:

6x³ - x²y² - 2xy³

Thus, the correct answer is option A.

To solve the problem:

We need to subtract (7x + 2) from (-6x + 8).

This can be rewritten as:

• (-6x + 8) – (7x + 2)

Now, distribute the negative sign:

• -6x + 8 – 7x – 2

Next, combine like terms:

• Combine the x terms: -6x - 7x = -13x
• Combine the constant terms: 8 - 2 = 6

The final result is:

-13x + 6

We need to subtract (3xy + 5yz – 7xz + 1) from (-4xy + 2yz – 2xz + 5xyz + 1).

Step 1: Write the subtraction expression:

(-4xy + 2yz – 2xz + 5xyz + 1) - (3xy + 5yz – 7xz + 1)

Step 2: Distribute the minus sign across the second set of terms:

= -4xy + 2yz – 2xz + 5xyz + 1 - 3xy - 5yz + 7xz - 1

Step 3: Combine like terms:

• For xy terms: -4xy - 3xy = -7xy
• For yz terms: 2yz - 5yz = -3yz
• For xz terms: -2xz + 7xz = 5xz
• For xyz term: 5xyz (no like term)
• For constants: 1 - 1 = 0

Step 4: Write the final expression:

5xz + 5xyz - 7xy - 3yz

Thus, the correct answer is:

a) 5xz + 5xyz - 7xy - 3yz