D. (a+b)(a +ab+b) 20. Find the factor of a P-b A. (a+b)(a-b) B. (a-b)(a +ab-b2) C.(a-b)(a’-ab-b?) D. 2a + 8 21 One of the factors of 2a?+ 5a - 12 is a + 4, what is the other factor? A. 2a - 3 B. 2a + 3 C. 2a - 8 D. -24 22. Which of the following values of k will make x? - 5x + k factorable? A. 5 B. 14 C. -10 23. Which of the following is a rational algebraic expression? 2cd+d 2a2 A. ava 3 x²-x-12 24. Which value of x is not allowed in the expression ? x² - 4 A. O B. 2. C. 4 2 Vy+44 D. 22 B. C. 5x1/3 D.6 x+5 1-√x 25. Is the expression a rational algebraic expression and why? A. Yes,
because it is expressed in a form of a fraction. B. Yes, because the numerator and the denominator are both polynomials. C. No, because x + 5 is not a polynomial. D. No, because 1 - Vă is not a polynomial. 26. The product of x multiplied by x? A 2x B. X2 27. Which two integer will give you a product of 16 and a sum of 10? DX? C. XX D. 4 and 4 C. 2 and 8 A. 5 and 5 B. 1 and 16 x² + 4x 28. Simplify: x+4 C. X + 1 D. 4x A.X B. 2x D. 6cd 24cd² 29. The greatest common factor of 18c2d A. 9c²d² B. 6c4d2 c. 9c²d x2-8x+16 30. When simplified, is x2-16 X-4 x-4 x+4 А. B. C. X x+4 X-4 16a"b7c5 31. What rational algebraic expression is equivalent to ? 48a4b8c3 a6-13 c3 B. C. 3 b х D. x+4 a 2 D 4 C2 3 x²7x+10 32. Jen was asked to simplify .Her solution is presented below x2-25 x2 - 7x+10 (x-2)(2-5) x²-25 (x-3)(x+5) (x-2) (x-3) 2 3 What makes her solution wrong? A. cancelling of x-5 B. crossing out x-5 C.X - 25 being factored out D. dividing out variable x
pa answer po ng ayos plsss kailangan ko na po ngayon
Share
Answer:
• When we add (or subtract) two algebraic expressions, the like terms
are added (or subtracted) and the unlike terms are written as they
are.
• To find the value of an expression, we substitute the values of the
variables in the expression and then simplify.
• Rules and formulas in mathematics are written in a concise and
general form using algebraic expressions.
In Examples 1 to 3, there are four options, out of which one is correct.
Write the correct answer.
Example 1: The like terms in 3x (3 – 2y) and 2 (xy + x2) are
(a) 9x and 2x2 (b) – 6xy and 2xy
(c) 9x and 2xy (d) – 6xy and 2x2
Solution : The correct answer is (b).
In words
A number x is increased by 7
A number y is decreased by 7
A number a is multiplied by 7
A number k is divided by 7
Expression
x + 7
y – 7
a × 7
k ÷ 7
Sometimes you might have to describe a real-life situation using a
mathematical expression.
You need to imagine what would happen to a quantity, and write that
down using variables, and +, –, × and ÷ .
15-04-2018
Example 2: The coefficient of xy in 3x2 zy + 7xyz – 2z2x is
(a) 3z (b) – 2 (c) 7yz (d) 7z
Solution: Correct answer is (d).
Example 3: The factors of the term –xy2 are
(a) x × y × y (b) – 1 × y × y
(c) – 1 × x × y (d) – 1 × x × y × y
Solution: Correct answer is (d).
Solution: Like terms
When you change a variable expression to a word expression you, can
say the same thing in several different ways.
+ : Instead of “2 added to x”, you could say “x increased by 2,” or
“2 more than x,” or “the sum of x and 2.”
– : “2 subtracted from x” means the same as “2 less than x,” or
“x decreased by 2.”
× : “x multiplied by 2” means the same as ”the product of x and 2,”
“x times 2,” or “twice x.”
÷ : you could say: either “x divided by 3” or “one third of x.”
15-04-2018
In Examples 8 to 10, state whether the statements are True or False.
Example 8: An expression with two terms is called a binomial.
Solution: True
Example 9: Every polynomial is a monomial.
Solution: False
Example 10: The value of a variable is fixed.
Solution: False
Example 11: Twice the sum of length x and breadth y of a rectangle is
the perimeter of a rectangle. Write the expression for
perimeter.
Solution: Perimeter of rectangle = 2 (Length + Breadth)
= 2 (x + y) = 2 x + 2 y
Example 12: Identify the term containing u2 in the expression
u3 + 3u2v + 3uv 2 + v3 and write its coefficient.
Solution: Term containing u2 = 3u2v
Coefficient of u2 = 3v
Any number not joined to a variable is called a constant – like the 4
above. It’s called that because its value doesn’t change, even if the value
of the variable changes.
A term is a group of numbers and variables. One or more terms added
together make an expression. For example, in the expression above, 2k is
one term and 4 is another term. In the expression 3 + 4x – 5wyz, the
terms are 3, 4x and – 5wyz.
Example 13: Simplify the expression by combining the like terms:
7x3 – 3x2y + xy2 + x2y – y3
Solution: Rearranging the terms in the given expression, we get
7x3 – 3x2y + x2y + xy2 – y3
= 7x3 + (– 3x2y) + x2y + xy2 – y3
= 7x3+(– 3 + 1) x2y + xy2 – y3 [Using distributive property]
= 7x3+(– 2) x2y + xy2 – y3
= 7x3– 2x2y + xy2 – y3
Example 14: Subtract the sum of – 3x3y2 + 2x2y3 and – 3x2y3 – 5y4
from x4 + x3 y2 + x2y3 + y4.
Expressions are mathematical phrases that may contain numbers,
operations and variables. The operations act like a set of instructions
that tell you what to do with the numbers and variables. For example,
2k + 4 tells you to double k, then add four to it.
There are two types of expressions – numeric and variable.
• Numeric expressions have numbers in them, and often operations –
but they don’t include any variables:
→ 5 + 13
→ 2 × 5 – 6
→ 8 + 7 ÷ 6
• Variable expressions have variables in them, and may also include
numbers and operations :
→ 5 h
→ 5 x
→ 5 k + 4
15-04-2018
Solution: – 3x3y2 + 2x2y3
+ – 3x2y3 – 5y4
– 3x3y2 – x2y3 – 5y4
Sum = – 3x3y2 – x2y3 – 5y4
Now, x4 + x3y2 + x2 y3 + y4
– 3x3y2 – x2y3 – 5y4
(+) (+) (+)
difference = x4 +4x3y2 + 2x2y3 + 6y4
Example 15: Find the value of the following expressions at a = 1 and
b = –2:
(i) a2 + b2 + 3ab (ii) a3 + a2b + ab2 + b3
Solution: (i) Value of a2 + b2 + 3ab at a = 1 and b = – 2
= (1)2 + (–2)2 + 3 (1)(–2)
= 1 + 4 – 6
= 5 – 6
= – 1
The parts of a variable expression that are separated by addition or
subtraction signs are called terms. The variable expression x + 3y + 2x – 4y2
contains four terms : x, 3y, 2x and – 4y2. The terms x and 2x are like terms
because they have the same variable raised to the same power. The terms
3y and 4y2 are unlike terms because they have different variable parts.
Variables are all well and good, but they’re only useful when you use them
to solve math problems. You can use variables and numbers to describe a
problem in math terms — it’s called an expression.
15-04-2018
(ii) Value of a3 + a2b + ab2 + b3 at a = 1 and b = – 2
= (1)3 + (1)2(–2)+(1) (–2)2 + (–2)3
= 1 – 2 + 4 – 8
= 5 – 10
= – 5
Answer:
huh? paki ayos naman po JAHABAHAJJbdbd