6. (x+3)(x – 3)-40 factorise it with difference of two sq.
Answers
Answer: Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
(x-3)*(x+3)-(40)=0
Step by step solution :
STEP
1
:
Equation at the end of step 1
(x - 3) • (x + 3) - 40 = 0
STEP
2
:
Trying to factor as a Difference of Squares
2.1 Factoring: x2-49
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 49 is the square of 7
Check : x2 is the square of x1
Factorization is : (x + 7) • (x - 7)
Equation at the end of step
2
:
(x + 7) • (x - 7) = 0
STEP
3
:
Theory - Roots of a product
3.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation:
3.2 Solve : x+7 = 0
Subtract 7 from both sides of the equation :
x = -7
Solving a Single Variable Equation:
3.3 Solve : x-7 = 0
Add 7 to both sides of the equation :
x = 7
Two solutions were found :
x = 7
x = -7
Answer:
using (a^2)-(b^2) = (a-b)(a+b) ...identity
Step-by-step explanation:
so.,
x^2 -9 -40
x^2-49
...answer=x-7.. and x+7
.
so by taking this equation as p(x)=x-7 or x+7
x-7=0. x+7=0
x=7. x=-7