Answer:
9y²
Step-by-step explanation:
The square of a binomial can be written as (a + b)². If you expand this formula, you get
(a + b)(a + b). Use F.O.I.L. to multiply this out..
F - stands for 'Firsts' (the first values in each set of parenthesis)
O - stands for 'Outsides' ( the first value in the first set of parenthesis, and the
second value in the second set of parenthesis)
I - stands for 'Insides' ( the second value in the first set of parenthesis, and
the first value in the second set of parenthesis)
L - stands for 'Lasts' ( the second value in each set of parenthesis)
This is the order you multiply them in...so we get
F - a² (a times a)
O - ab
I - ba (which we rewrite as ab, since order doesn't matter when multiplying)
L - b²
We add them together to get a² + ab + ab + b²
which simplifies to a² + 2ab + b²
Read this as, the square of the first term in the parenthesis (a²), plus twice the product of the terms (2ab is twice the product of a and b), plus the square of the last term in the parenthesis)
So to solve this we need to know what makes 16x^2+24xy + ∗ factor into some form of (a + b)².
Look at the bold paragraph above and work backwards.
Take the square root of the term 16x², which is 4x. That goes in the first value of the parenthesis, so we have
(4x + c)²
We know that 24xy is twice the product of the two terms, so we divide by 2 to see the product of the two terms.
24xy/2 = 12xy,
We know one term, so divide 12xy by the first term, 4x to find the second term.
12xy/4x = 3y
So the last term in our set of parentesis is 3y, so we have
(4x + 3y)²
To get the missing value, square the second term, (3y)² = 9y²
So 9y² is our missing term.
16x^2+24xy + 9y² = (4x + 3y)²
