State whether the statements given are True or False.

4p is the numerical coefficient of q² in – 4pq².

Use the given algebraic expression to complete the table of number patterns.

Observe the patterns of digits made from line segments of equal length. You will find such segmented digits on the display of electronic watches or calculators.

(a)

(b)

(c)

If the number of digits formed is taken to be n, the number of segments required to form n digits is given by the algebraic expression appearing on the right of each pattern.

How many segments are required to form 5, 10, 100 digits of the kind

Write the coefficient of x2 in the following:

(i) x² – x + 4

(ii) x³ – 2x² + 3x + 1

(iii) 1 + 2x + 3x² + 4x³

(iv) y + y²x + y³x² + y⁴x³

Find the numerical coefficient of each of the terms:

(i) x³y²z, xy²z³, –3xy²z³, 5x³y²z, –7x²y²z²

(ii) 10xyz, –7xy²z, –9xyz, 2xy²z, 2x²y²z²

State whether the statements given are True or False.

In like terms, the numerical coefficients should also be the same.

Simplify the following by combining the like terms and then write whether the expression is a monomial, a binomial or a trinomial.

(a) 3x²yz² – 3xy²z + x²yz² + 7xy²z

(b) x⁴ + 3x³y+3x²y²–3x³y–3xy³+y⁴– 3x²y²

(c) p³q²r + pq²r³ + 3p²qr² – 9p²qr²

(d) 2a + 2b+2c–2a–2b–2c – 2b + 2c + 2a

(e) 50x³ – 21x + 107 + 41x³ – x + 1 – 93 + 71x–31x³

State whether the statements given are True or False.

5a and 5b are unlike terms.

State whether the statements given are True or False.

4p is the numerical coefficient of q² in – 4pq².

State whether the statements given are True or False.

In like terms, variables and their powers are the same.

Translate each of the following algebraic expressions