Answer:
36p²
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 *−42pq+49q^2 factor into some form of (a + b)².
Look at the bold paragraph above and work backwards.
Take the square root of the term 49q², which is 7q. That goes in the second value of the parenthesis, so we have
(c - 7q)² (there is a subtraction sign because it's -42pq)
We know that 42pq is twice the product of the two terms, so we divide by 2 to see the product of the two terms.
42pq/2 = 42pq,
We know one term, so divide 42pq by the second term, 7q to find the first term.
42pq/7q = -6p
So the first term in our set of parenthesis is -6p, so we have
(6p - 7q)²
To get the missing value, square the first term, (6p)² = 36p²
So 36p² is our missing term.
16x^2+24xy + 9y² = (4x + 3y)²
