Analyze the given algebraic expressions by determining their number of terms, constant term, coefficient of x, degree, and value when x = -2 and y = -2.

QUESTION 1

Expression	Number of terms	Constant term	Coefficient of $x$	Degree of the expression	Value of expression if $x = -2$ and $y = -2$
$3x^2 + 5 + 6x - 7y$	4	5	6	2	19
$56xy + 82y^2 - 13x - 15$	4	-15	-13	2	563
$8x^4 + x^2 - 7$	3	-7	0	4	125

Calculations for Question 1:

Expression 1: $3x^2 + 5 + 6x - 7y$

• Number of terms: $3x^2$, 5, $6x$, $-7y$. There are 4 terms.
• Constant term: 5.
• Coefficient of $x$: 6.
• Degree of the expression: The highest power is $x^2$, so the degree is 2.
• Value if $x = -2, y = -2$: $$3(-2)^2 + 5 + 6(-2) - 7(-2)$$ $$= 3(4) + 5 - 12 + 14$$ $$= 12 + 5 - 12 + 14$$ $$= 19$$

Expression 2: $56xy + 82y^2 - 13x - 15$

• Number of terms: $56xy$, $82y^2$, $-13x$, $-15$. There are 4 terms.
• Constant term: $-15$.
• Coefficient of $x$: $-13$.
• Degree of the expression: The highest sum of powers in a term is $1+1=2$ for $56xy$ and 2 for $82y^2$, so the degree is 2.
• Value if $x = -2, y = -2$: $$56(-2)(-2) + 82(-2)^2 - 13(-2) - 15$$ $$= 56(4) + 82(4) + 26 - 15$$ $$= 224 + 328 + 26 - 15$$ $$= 552 + 26 - 15$$ $$= 578 - 15$$ $$= 563$$

Expression 3: $8x^4 + x^2 - 7$

• Number of terms: $8x^4$, $x^2$, $-7$. There are 3 terms.
• Constant term: $-7$.
• Coefficient of $x$: There is no $x$ term, so the coefficient is 0.
• Degree of the expression: The highest power is $x^4$, so the degree is 4.
• Value if $x = -2, y = -2$: (Note: $y$ is not in the expression) $$8(-2)^4 + (-2)^2 - 7$$ $$= 8(16) + 4 - 7$$ $$= 128 + 4 - 7$$ $$= 132 - 7$$ $$= 125$$

QUESTION 2

2.1 State whether the following expressions are monomial, binomial, or trinomial.

2.1.1 $(2x+7) \times (3x^2+2x-1)$