Multiply two binomials: special cases
key notes:
Difference of squares:
(a+b)(aāb)=a2āb2
Square of a binomial:
- (a+b)2=a2+2ab+b2
- (aāb)2=a2ā2ab+b2
Learn with an example
š Find the product.
Simplify your answer.
(2v+2)(2vā2)
(2v+2)(2vā2) is the difference of squares, just like (a+b)(aāb). So, you can find (2v+2)(2vā2) with this formula:
(a+b)(aāb)=a2āb2
Replace a with 2v and b with 2, then simplify.
(2v+2)(2vā2)
(2v)2ā22
4v2ā4
š Find the product.
Simplify your answer.
(d+3)(dā3)
(d+3)(dā3) is the difference of squares, just like (a+b)(aāb). So, you can find (d+3)(dā3) with this formula:
(a+b)(aāb)=a2āb2
Replace a with d and b with 3, then simplify.
(d+3)(dā3)
d2ā32
d2ā9
š Find the square.
Simplify your answer.
(2k+3)2
(2k+3)2 is the square of a binomial, just like (a+b)2. So, you can find (2k+3)2 with this formula:
(a+b)2=a2+2ab+b2
Replace a with 2k and b with 3, then simplify.
(2k+3)2
(2k)2+2(2k)(3)+32
4k2+12k+9
let’s practice!šļø