how would you factorise
a) 9x^2 - 49
b) 9x^2 - 121
c) 49x^2 - 25x^2
thankyou
Look up "difference of squares"
Each of your questions is a basic example of that type.
To factorize the given expressions, we need to express them as the product of two or more simpler expressions. Let's go through each expression one by one:
a) 9x^2 - 49:
This is a difference of squares expression. Recall that the difference of squares formula is: (a^2 - b^2) = (a + b)(a - b).
Applying this formula, we can rewrite 9x^2 - 49 as follows:
9x^2 - 49 = (3x)^2 - 7^2
Now, we notice that we have a difference of squares:
= (3x + 7)(3x - 7)
Therefore, the factorization of 9x^2 - 49 is:
9x^2 - 49 = (3x + 7)(3x - 7)
b) 9x^2 - 121:
Similar to the previous example, this is also a difference of squares expression.
Rewriting the expression:
9x^2 - 121 = (3x)^2 - 11^2
Again, we recognize that we have a difference of squares:
= (3x + 11)(3x - 11)
Thus, the factorization of 9x^2 - 121 is:
9x^2 - 121 = (3x + 11)(3x - 11)
c) 49x^2 - 25x^2:
In this case, we are given a subtraction of two squares expressions.
49x^2 - 25x^2 = 7x^2 - 5x^2
When subtracting or adding like terms, we combine the coefficients of like terms while keeping the variable part unchanged:
= (7 - 5)x^2
= 2x^2
Therefore, the factorization of 49x^2 - 25x^2 is:
49x^2 - 25x^2 = 2x^2