Math - Reviewer For Grade 7
Math - Reviewer For Grade 7
Math - Reviewer For Grade 7
Algebraic expression – a statement containing one or more terms connected by a plus or minus sign.
Variable – is a symbol which represents any number from a given replacement set, used to
represent an unknown value.
Term – can be a variable or a signed number multiplied to a variable or a constant and each term is
separated by a sign, plus or minus.
Literal coefficient – is a variable used to represent a number and it may be raised to power.
Mathematical expression – is a phrase or sentence that has a minimum of two numbers, has at least
one arithmetic operation, and a letter that show a value of something.
Polynomial – an algebraic expression that has one or more terms. Derived from “poly” meaning
many, “nomial” meaning parts or terms.
Kinds of polynomials
Degree Name
0 Constant
1 Linear
2 Quadratic
3 Cubic
4 Quartic
5 Quintic
Ex. 2³ = 0 degree ↓
Because 2 is a constant.
Remember:
In algebraic expressions, we replace the specified value of a variable in the expression.
After that, simplify the expression into a single numerical value.
Ex.
3 (g + 7) g=2
3 (2 + 7)
3 (9)
27
Remember:
Follow GEMDAS rule.
Adding Polynomials
Combining similar terms in the expressions. To combine the terms, add the numerical
coefficients and copy the common literal coefficient.
Ex.
(2x + 6) + (3x² + 5x + 1)
HORIZONTAL METHOD
2x + 6 + 3x² + 5x + 1
3x² + 2x + 5x + 6 + 1
3x² + 7x + 7
(2x + 6) + (3x² + 5x + 1)
VERTICAL METHOD
3x² + 2x + 6
5x 1
3x² + 7x + 7
Subtracting Polynomials
Change the signs of all the terms in the subtrahend then proceed to the rule of addition.
Product Rule – when multiplying powers with the same base, copy the base then add the
exponent.
Ex. 2² · 2³ = 2⁵ = 256
Power of a Product Rule – To find the power of a power, copy the base then multiply the
two exponents.
Ex. (a³)² + a 3 · 2 = a⁶
Ex. a⁰ = 1
Negative Exponent – a nonzero base raised to a negative exponent is equal to the reciprocal
of the base raised to the positive exponent.
Denominator is always 1.
Multiplication of Polynomials
To multiply a monomial with another monomial, simply multiply the numerical coefficients
then multiply the literal coefficients by applying the basic laws of exponents.
To multiply a monomial with a polynomial, simply apply the distributive property and follow
the rule in multiplying mono by mono.
Ex.
Polynomial by Polynomial
FOIL method
First
Outer
Inner
Last
Ex.
Binomial by Trinomial
Ex.
Polynomial by Polynomial
Ex.
Special products
Ex. (x + 6)²
(x)² + 2(x)(6) + (6)²
x² + 12x + 36
Ex. (x + y + z)²
(x)² + (y)² + (z)²
2 (x)(y)
2 (x)(z)
2 (y)(z)
x² + y² + z² + 2xy + 2xz + 2yz
Steps in cubing a binomial
1. Find the cube of each to each the first and the last terms
2. The second term is three times the product of the square of the first term and the
second term
3. The third term is three times the product of the first term and the square of the last
term.
Ex. (c + 2)³
(c)³ + (2)³
3 (c)²(2)
3 (c)(2)²
c³ + 8 + 6c² + 12c