Here in this post, ill teach you how to operate factorized quadratic expression.We all know that factors are numbers.There are a lots of student out there that always get it odd to deal with factorization of quadratic expression. Here, i have full assurance for you when it come this operation.
The expression( x + 3)(x - 4) simply means( x + 3) x (x - 4). This means, the product of the two binomials ( x + 3) and (x - 4) is considered by multiplying each term in the first binomial by each term in the second binomial.
Lets look at some exercise to see how we can solve issues on factorization of quadratic operation.
Example I
1. Find the product of (y + 2) and (y - 5)
(y + 2) (y - 5) = y(y + 2 ) - 5 (y + 2) - x + = -
= y² + 2y -5y - 10
= y² - 3y - 10
The above operations is based on multiplying the variables in the brackets.There are two brackets in the operation, but the RHS brackets variables are to multiply with the LHS variables. I mean (y - 5), y will multiply (y + 2) before 5 also multiply (y + 2) then you collect like terms.
2. Expand (2c - 4m) and (c - 3m)
(2c - 4m)(c - 3m) = c (2c - 4m) - 3m( 2c - 4m)
= 2c² - 4cm - 6cm + 12m² --- - + - = -
= 2c² - 11cm + 12m²
The previous example shows that, c(c) means c x c = c² ,also do not forget the letters should be arranged in order.In a , c,v,h,e: a , b , c, e then v.I should strongly believed you understand my point.
3. Expand ( 4a + 2)²
( 4a + 2)² = ( 4a + 2) ( 4a + 2)
= 4a ( 4a + 2) + 2 ( 4a + 2)
= 16a² + 8a + 8a + 4
= 16a² + 16a + 4
In mathematics any variables raised to power 2 is that variables into 2 places.I mean, a² = a x a,the same as: (3)² = 3 x 3 = 9.
Expand each expression.Arrange the working a the above examples..
1. (a + 2)(a + 3)
2. (c + 6)(c - 1)
3.(5p - 2e)(5p + 3e)
4. (u + 2v)(u + 3v)
Solution
1. (a + 2)(a + 3)
(a + 2)(a + 3) = a(a + 2) + 3(a + 2)
= a² + 2a + 3a + 6
= a² + 5a + 6
2. (c + 6)(c - 1)
(c + 6)(c - 1) = c (c + 6) - 1 (c +6)
= c² + 6c - c - 6
= c² + 5c -1
Remember, anything multiply by 1 is that thing. I mean, 1 x e =e , 1 x 0 = 0 also 1 x( -6)=6.
3.(5p - 2e)(5p + 3e)
(5p - 2e)(5p + 3e) = 5p (5p - 2e) + 3e (5p - 2e)
= 25p² - 10ep + 15ep - 6e²
= 25p² + 5ep - 6²
Remember -10 + 15 =5
4. (u + 2v)(u + 3v)
(u + 2v)(u + 3v) = u (u + 2v) + 3y (u + 2v)
= u² + 2uv + 3uy + 6vy
I should belief my explanation is well cleared
Activities
Expand each expression.Arrange the working a the above examples..
i. (p - 3)(p - 7)
ii. (2x - 1)²
iii. (2c - 9)(4c + 5e)
iv. (2a - 1)(a + 4)
All the above expressions are very simple, if only you follow up my instructions and the rules involved in this operations.please if you have questions, please put them in the comments box.
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