Question
What do we get after expanding (p + 3q - 2z)2?
- p2 + 9q2 + 4z2 + 6pq – 12qz + 4zp
- p2 + 9q2 + 4z2 + 12pq + 12qz + 4zp
- p2 + 9q2 + 4z2 – 12pq – 12qz – 4zp
- p2 + 9q2 + 4z2 + 6pq – 12qz – 4zp
The correct answer is: p2 + 9q2 + 4z2 + 6pq – 12qz – 4zp
We know that (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
(p + 3q - 2z)2can also be written as (p + 3q + ( - 2z))2.
Here, a = p, b = 3q and c = - 2z
Therefore, using that formula we get (p + 3q + ( - 2z))2
= p2 + (3q)2 + ( - 2z)2 + 2(p)(3q) + 2(3q)( - 2z) + 2( - 2z)(p)
= p2 + 9q2 + 4z2 + 6pq – 12qz – 4zp.
= p2 + (3q)2 + ( - 2z)2 + 2(p)(3q) + 2(3q)( - 2z) + 2( - 2z)(p)
Related Questions to study
What do we get after factoring 49x2 - 28xy + .4y2?
What do we get after factoring 49x2 - 28xy + .4y2?
_______ is a factor of 4x2 - 9x + 5.
_______ is a factor of 4x2 - 9x + 5.
Expand.
![left parenthesis 2 x plus y right parenthesis cubed](data:image/png;base64,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)
Expand.
![left parenthesis 2 x plus y right parenthesis cubed](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEEAAAASCAYAAAAE7bMcAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAPUJuPDwAAAfdJREFUeNpjYBg54D8U/wLiC0DshkthFhB3DHHPdkD9gQ9oAPFDbBJ6QHx8mMT6Uah/cAEmIH6HS6MBEt8aiNcA8SekJBQ9RALBGIgP45ATBuIpQJyILmEADQRkcBCII4GYB8rXgqqJHCIBcRgaGNjKhVhsGrqAOIcIg+WB+BINCy5qgjwc5RsfELcCcRq6xA4gtiXS8B9YxJJxWNgMlaNmIMwF4nAs4gVQz8GAJRDvJcUfoHzPRoQDLLFkGxg4B8TiSPxEaN6jdkqIh6ZcZMAFxLeg+R0G2KD+wgZAEX4GXfAPEZZzAPFJaIGJDXgAcR+U7UIgFigJBC8gXoUmVg/EtVjU/sJSHvyApnx5UgNBEIg34GtgQMFuILaH1iTCRDZe8GFcpfsVJL4oEN+FRhK+QCAI8GUHJWgAqBBhTgHUYj0aF4zfkNh9UHvRAb7sgDMGrXG0rGZD8xwhAGtX9JFZjZISCIehkaMETQVMOMovkrIktipSHJr3WIjQD3LMJmhg8UALHWEaBsJCIPYD4qW46nyof7pIcQC2xtIWaEogBEB5chuap32AeDENA6EAWlVeIrGxRBAcR8vLxBRYoHy3DoilsZi3HFpj0AIEQN3hR0azGS8YSh0oPwJuJdSBwgsyhkhXehu04MNVvqUN98ERHWh5RTUAALZ4eX0lxGrrAAAAknRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbz4oPC9tbz48bW4+MjwvbW4+PG1pPng8L21pPjxtbz4rPC9tbz48bWk+eTwvbWk+PG1zdXA+PG1vPik8L21vPjxtbj4zPC9tbj48L21zdXA+PC9tYXRoPrtBvtQAAAAASUVORK5CYII=)
Find the first four terms of the expansion
.
Find the first four terms of the expansion
.
Expand using the binomial theorem.
![left parenthesis 1 plus x right parenthesis squared](data:image/png;base64,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)
Expand using the binomial theorem.
![left parenthesis 1 plus x right parenthesis squared](data:image/png;base64,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)
Use polynomial identities to factor each polynomial
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Expand.
Expand.