Question

Find the product of \[(3a - 4)(3a + 4)\]?

Answer 1

Hint: We simplify or solve the product given by multiplying numbers in the first bracket with the complete second bracket one by one. We multiply the given factors or brackets by opening the terms and then write the quadratic equation formed by multiplication.
When we have to multiply the brackets like \[(a + b)(c + d)\]then we multiply the second bracket by a first and then by b i.e. \[a(c + d) + b(c + d)\]. Then we multiply each term outside the bracket with terms inside the bracket one by one i.e. a with c, a with d, b with c and b with d i.e. \[ac + ad + bc + bd\].

Complete step by step answer:
We are given the product \[(3a - 4)(3a + 4)\]
We will simplify the product by multiplying terms from first bracket to second bracket one by one.
\[ \Rightarrow (3a - 4)(3a + 4) = 3a(3a + 4) - 4(3a + 4)\]
Now we multiply each term outside the bracket with terms inside the bracket one by one
\[ \Rightarrow (3a - 4)(3a + 4) = \left( {3a \times 3a} \right) + \left( {3a \times 4} \right) - \left( {4 \times 3a} \right) - \left( {4 \times 4} \right)\]
Calculate the products on right side of the equation
\[ \Rightarrow (3a - 4)(3a + 4) = 9{a^2} + 12a - 12a - 16\]
Cancel terms having same magnitude and opposite signs
\[ \Rightarrow (3a - 4)(3a + 4) = 9{a^2} - 16\]
\[\therefore \]Solution of \[(3a - 4)(3a + 4)\] is \[9{a^2} - 16\]

Note: Alternate method:
We have to find the product of \[(3a - 4)(3a + 4)\]
Since we know the identity \[(a - b)(a + b) = {a^2} - {b^2}\]
This product is similar to the identity as we have subtraction and addition of the same terms in both brackets.
We can write \[(3a - 4)(3a + 4) = {(3a)^2} - {(4)^2}\]
Square the terms on right hand side of the equation
\[(3a - 4)(3a + 4) = 9{a^2} - 16\]
\[\therefore \]Solution of \[(3a - 4)(3a + 4)\] is \[9{a^2} - 16\]