The answer to the equation is 16x^2 + 40x + 25.
How did 40x come into the equation?
How did 40x come into the equation?
-
Use FOIL.
(4x + 5)^2
= (4x + 5)(4x + 5)
= (4x)*(4x) + (4x)*(5) + (5)*(4x) + (5)*(5)
= 16x^2 + 20x + 20x + 25
= 16x^2 + 40x + 25
40x comes from adding "20x + 20x" when you FOIL out each term.
(4x + 5)^2
= (4x + 5)(4x + 5)
= (4x)*(4x) + (4x)*(5) + (5)*(4x) + (5)*(5)
= 16x^2 + 20x + 20x + 25
= 16x^2 + 40x + 25
40x comes from adding "20x + 20x" when you FOIL out each term.
-
When you square something it means you are multiplying it by itself, so (4x+5)^2 is the same as
(4x+5)(4x+5).
to multiply these you have to distribute. so the 4x in the first parentheses has to multiply the 4x and the 5 in the second parentheses. and the 5 from the first parenthese has to multiply the 4x and the 5 in the second parentheses.
(4x+5)(4x+5).
to multiply these you have to distribute. so the 4x in the first parentheses has to multiply the 4x and the 5 in the second parentheses. and the 5 from the first parenthese has to multiply the 4x and the 5 in the second parentheses.
-
In addition to all the previous answers, you should try to memorize the perfect square formulas. It will save you time on the test.
(a ± b)^2 = a^2 ± 2ab + b^2
Compare with the given formula, a=4x and b=5.
The middle term of 2ab gives 40x.
(a ± b)^2 = a^2 ± 2ab + b^2
Compare with the given formula, a=4x and b=5.
The middle term of 2ab gives 40x.
-
(4 x + 5)^2
= (4 x + 5) (4 x + 5)
= 4 x(4 x + 5) + 5 (4 x + 5)
= 16 x^2 + 20 x + 20 x +25
= 16 x^2 + 40 x + 25
= (4 x + 5) (4 x + 5)
= 4 x(4 x + 5) + 5 (4 x + 5)
= 16 x^2 + 20 x + 20 x +25
= 16 x^2 + 40 x + 25
-
(4x+5)^2 = (4x+5)(4x+5)
= 16x^ + 20x + 20x + 25
=16x^ + 40x + 25
= 16x^ + 20x + 20x + 25
=16x^ + 40x + 25