High School

Factor the following expression:

\[ y^2 - 16y + 64 = 128 \]

Find the common factor of \(5x\) and \(15y\).

If the cost of 1 kg of mango is ₹60, what would be the cost of 5 kg of mangoes?

Answer :

Let's break down the given parts of the question one by one.


  1. Factorise: [tex]y^2 - 16y + 64 = 128[/tex]

    First, let's bring all terms to one side of the equation:

    [



y^2 - 16y + 64 - 128 = 0
]

Simplifying inside the equation gives:

[tex]y^2 - 16y - 64 = 0[/tex]

Now, we need to factor the quadratic equation. Let's find two numbers that multiply to [tex]-64[/tex] and add up to [tex]-16[/tex].

Those numbers are [tex]-8[/tex] and [tex]-8[/tex]:

[tex](y - 8)(y - 8) = (y - 8)^2 = 0[/tex]

So, the factorised form of [tex]y^2 - 16y + 64 = 128[/tex] is [tex](y - 8)^2 = 0[/tex].


  1. Find the common factor of [tex]5x[/tex] and [tex]15y[/tex]

    To find the common factor, we first look at the coefficients of the terms:


    • The coefficient of [tex]5x[/tex] is 5.

    • The coefficient of [tex]15y[/tex] is 15.


    The greatest common factor (GCF) of 5 and 15 is 5.

    Therefore, the common factor of [tex]5x[/tex] and [tex]15y[/tex] is 5.


  2. If the cost of 1 kg of mango is [tex]\text{₹}60[/tex], then what would be the cost of 5 kg mango?

    To find the cost of 5 kg, we multiply the cost of 1 kg by 5:

    [



\text{Cost of 5 kg} = 60 \times 5 = 300
]

Hence, the cost of 5 kg of mango is [tex]\text{₹}300[/tex].