Question

How do you simplify $3(5 + 5x)?$

Answer 1

Hint: As we know that to multiply means to increase in number especially greatly or in multiples. We know that the standard form of any quadratic expression is $a{x^2} + bx + c$. Here in this question we have to find the product by using distributive property, we just multiply each term of the first polynomial by each term of the second polynomial and then simplify by combining terms like adding coefficients, and then combine the constants.

Complete step-by-step solution:
Here we have $3(5 + 5x)$, we will now expand the expression by using the distributive property. The distributive property says that if there is $a(b + c)$, then we can expand it as $ab + ac$. We must ensure that each term in the second bracket is multiplied by each term in the first bracket.
This can be done as follows: $3(5 + 5x) = 3 \times 5 + 3 \times 5x$.
Now by multiplying each term of the above expression we get: $15 + 15x$
We can also write it as $15(1 + x)$
As we know that the standard form of expression is of the form $a{x^2} + bx + c$.
Hence the product and of the required expression is $15x + 15$.

Note: We should note that while solving this kind of question we need to expand the term with the help of distributive property. Also we should be careful while adding or subtracting with the negative and positive signs. We know that the standard form means writing the expression starting with the term which has the highest power of variable. In this case $x$ has the highest power and then continues with the last term.