Please help me with these factorise algebra questions!!!
1. 9c squared + 30c + 25 - 4d squared
2. 12 + 89 - 4a squared
3. -5x squared + 27x - 10
4. If A= 15x squared - 20x +11 and
B= 1 + 9x+ 5x squared, then A-B when factorised is...
Online, an exponent is indicated by "^", for example, x^2 = x squared.
3. To factor, factor the end terms into two factors (5,-1 or -5,1) and (10, -1 or -10,1 or 5,-2 or -5,2). See which products of the two end terms will add to the center term value.
In this case, (-5x+2)(x-5)
4. 15x^2 -20x + 11 - 1 - 9x -5x^2
Combine like terms and then go through the process indicated for #3.
1. Is there a typo here, the "d" term?
2. If there is no typo here, the two products of the end factor should cancel each other out leaving no middle term.
It would help if you proofread your questions before you posted them.
9c 2
Sure! I would be happy to help you with these factorization questions. Here's how you can factorize each expression step by step:
1. To factorize 9c^2 + 30c + 25 - 4d^2:
First, notice that the expression has four terms. We can group them into two separate binomials.
(9c^2 + 30c) + (25 - 4d^2)
Now, let's focus on each binomial individually:
For the first binomial, factor out the greatest common factor (GCF) from the terms 9c^2 and 30c:
9c^2 + 30c = 3c(3c + 10)
For the second binomial, notice that it is a difference of squares (25 - 4d^2).
A difference of squares can be factorized as the product of the sum and difference of the square roots:
25 - 4d^2 = (5 + 2d)(5 - 2d)
Putting it all together, the factorization of 9c^2 + 30c + 25 - 4d^2 is:
3c(3c + 10) + (5 + 2d)(5 - 2d)
2. To factorize 12 + 89 - 4a^2:
Similar to the previous example, first rearrange the terms into two separate binomials:
(12 + 89) - 4a^2
For the first binomial, simply combine 12 and 89:
12 + 89 = 101
For the second binomial, notice that it is a difference of squares:
4a^2 = (2a)^2
It can be factorized as:
4a^2 = (2a)(2a)
Putting it all together, the factorization of 12 + 89 - 4a^2 is:
101 - (2a)(2a)
Or in a more simplified form:
101 - 4a^2
3. To factorize -5x^2 + 27x - 10:
First, look for factors of -5 and -10 that add up to the coefficient of the linear term (27x). In this case, the factors are 5 and 2:
-5x^2 + 27x - 10 = -5x^2 + 5x + 22x - 10
Now, group the terms together so you can factor by grouping:
(-5x^2 + 5x) + (22x - 10)
Notice that the first two terms have a common factor of x and the second two terms have a common factor of 2:
x(-5x + 5) + 2(11x - 5)
Finally, factor out the common factors from each binomial:
x(-5x + 5) + 2(11x - 5) = x(-5(x - 1)) + 2(11x - 5)
4. To find A - B and factorize it:
Given A = 15x^2 - 20x + 11 and B = 1 + 9x + 5x^2
To find A - B, simply subtract the expressions:
A - B = (15x^2 - 20x + 11) - (1 + 9x + 5x^2)
Combine the like terms:
A - B = 15x^2 - 5x^2 - 20x + 9x + 11 - 1
Simplify further:
A - B = 10x^2 - 11x + 10
Since A - B does not have any common factors that can be factored out further, the factorized form of A - B is:
10x^2 - 11x + 10
I hope this helps! Let me know if you have any further questions.