Hey, if anyone is Free, May you please Solve the question in Picture Above, Please ^ ^
Question 1st: Show the Terms and Factors by the tree Diagram.
a: xy+7x²y²
b: (See picture above)
Answers
Question:
1) Show the terms and factors by the tree diagram.
a) xy + 7x²y²
b) -ab + 2b² - 3a²
c) 5xy² + 7²y
d) 13y² - 8x²y
2) Write all laws of exponents.
Answer:
Refer the attachment for tree diagram!
Step-by-step explanation:
An algebraic expression is an expression or combination of terms, variables, constants, coefficients, and arithmetic operations (addition "+", subtraction "-", multiplication "×", division "÷" etc.).
Let's take an example or expression to understand this: 5x + 3y + 1 [term 5x is a product of 5 & x (factors: numbers or variables that are multiplied to form a term i.e. 5 & x. And 5 is the coefficient of the term as it is a numerical factor of the term). Similarly, term 3y is a product of 3 & y. And both the terms add to form an algebraic expression] is an algebraic expression. Because it can be expressed in the form of terms, factors and coefficients. Also, there are two operations one is multiplication between 5 & x or 3 & y and other is addition between two terms & constant.
The parts of above expression are: 5 & 3 are coefficients, 5x & 3y are terms (product of two or more variables or number), x & y are variables and 1 is constant.
Note: “If the terms contain the same variable and same raised to the power then such type of terms are known as Like Terms and if not then such type of terms are known as Unlike Terms.”
Back to the question ;P
1) Show the terms and factors by the tree diagram. (Tree diagram: way to find or to represent the terms and factors in the form of tree.)
a) xy + 7x²y²
The terms are xy, 7x²y². Factors of xy are x & y and factors of 7x²y² are 7, x, x, y & y.
b) -ab + 2b² - 3a²
The terms are -ab, 2b² and - 3a². Factors of -ab are -a & b; factors of 2b² are 2, b & b and factors of -3a² are -3, a, & a.
c) 5xy² + 7x²y
Terms are 5xy² and 7x²y. Factors of 5xy² are 5, x, y & y and factors of 7x²y are 7, x, x & y.
d) 13y² - 8x²y
Terms are 13y² and -8x²y. Factors of 13y² are 13, y & y and factors of -8x²y are -8, x, x & y.
2) Write all laws of exponents. (Used for easy understanding. Also it tells how many times to multiply the base number.)
- a^p × a^q (here, a is base and p & are exponents) = a^(p + q)
- (a^p)^q = a^pq
- a^p/a^q = 1/a^(q - p) or a^(p - q)
- (a/b)^p = a^p/b^p or (ab)^p = a^p b^p
