1. Factorise the following binomials :
(i) 15m + 10n (ii) 9a2– 16
Answers
Step-by-step explanation:
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 : 9 is the square of 3
Check : 16 is the square of 4
Check : a2 is the square of a1
Factorization is : (3a + 4) • (3a - 4)
Equation at the end of step
2
:
(3a + 4) • (3a - 4) = 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 : 3a+4 = 0
Subtract 4 from both sides of the equation :
3a = -4
Divide both sides of the equation by 3:
a = -4/3 = -1.333
Solving a Single Variable Equation:
3.3 Solve : 3a-4 = 0
Add 4 to both sides of the equation :
3a = 4
Divide both sides of the equation by 3:
a = 4/3 = 1.333
Two solutions were
1)10+15 =25
total answer 25mn