factorise a^4-(b+c)^4
Answers
Step-by-step explanation:
<!DOCTYPE html>
<html lang=en>
<head>
<title>Shin Chan</title>
<style>
body {
background:#FF0000
}
.face {
height: 600px;
width: 350px;
position: relative;
margin: auto;
}
.face:before {
content:'';
background:black;
height:122px;
width:95px;
position:absolute;
z-index:6;
left:210px;
top:29px;
border-radius:100% 190% 100% 0%;
transform: rotate(-20deg);
}
.face:after {
content:'';
width:230px;
height:180px;
background:black;content:'';
transform: rotate(-8deg);
position:absolute;
border-radius:100% 160% 100% 0%;
left:70px;
bottom:-14px;
top:10px;
z-index:5;
}
.forhead, .forhead:after {
content: '';
width: 220px;
height: 181px;
background: #fbc6a3;
content: '';
transform: rotate(-3deg);
position: absolute;
border-radius: 60% 120% 50% 0%;
left: 67px;
bottom: -14px;
top: 21px;
z-index: 6;
}
.forhead:after {
width: 160px;
height: 150px;
border-radius: 150% 174% 159% 100%;
transform: rotate(-20deg);
top: 13px;
left: 59px;
border-top: 15px solid #fbc6a3;
}
.forhead:before{
background:#fbc6a3;
width:60px;
height:10px;
content:'';
position:absolute;
z-index:7;
left:105px;
top:9px;
transform: rotate(13deg);
border-radius:100%
}
.ear {
width:60px;
height:50px;
background:#fbc6a3;
z-index:7;
position:absolute;
border-radius:300% 190% 200% 100%;
transform: rotate(-20deg);
top:110px;
left:285px
}
.cheeks {
background: #fbc6a3;
width: 280px;
height: 100px;
border-radius: 50px 0px 50px 40px;
transform: rotate(-3deg);
position: relative;
content: 'a';top: 108px;
left:10px
}
.cheeks:after {
width: 297px;
height: 100px;
background: #fbc6a3;
content: '';
transform: rotate(-3deg);
position: absolute;
border-radius: 100% 100% 100% 100%;
left: 1px;
bottom: -14px;
}
.eye {
width:40px;
height:40px;
position:relative;
background:black;
border-radius:100%;
animation: close-eye 4s none .2s infinite;
}
.eye:after {
content:'';
position:absolute;
background:white;
width:15px;
height:15px;
border-radius:100%;
left:17px;
top:12px;
}
.eye:before {
content:'';
position:absolute;
width:70px;
height:60px;
border-radius:100%;
border-top:2px solid black;
left:-20px;
margin-top:-20px;
}
.eye.left,.eye.right {
position:absolute;
top:80px;
left:100px;
z-index:10;
}
.eye.right {
left:190px;
top:90px;
}
.eyebrow {
animation: eyebroani 2s linear .2s infinite;
}
.eyebrow,.eyebrow:after {
position:absolute;
width:20px;
height:60px;
background:black;
z-index:8;
border-radius:15px;
transform: rotate(40deg);
top:10px;
left:90px;
}
.eyebrow:after {
content:'';
transform: rotate(-100deg);
left:19px;
margin-top:-23px;
top:auto;
}
.eyebrow.right {
left:180px;
top:8px;
transform:rotate(50deg);
}
.mouth {
position:absolute;
width:40px;
height:40px;
background:#76322f;
border-radius:100%;
top:180px;
left:50px;
z-index:8;
}
.shy {
position:absolute;
width:0px;
height:0px;
border-radius:100%;
opacity:0;
box-shadow: 0px 0px 40px 20px red;
z-index:8;
left:35px;
top:160px;
animation: shy 10s linear .2s infinite;
}
.shy.right {
left:170px;
top:180px;
}
@keyframes eyebroani {
0% {margin-top:auto}
10% {margin-top:-10px}
20% {margin-top:auto}
30% {margin-top:-10px}
40% {margin-top:auto}
100% {margin-top:auto}
}
@keyframes shy {
0% {opacity:0}
10% {opacity:0.2}
90% {opacity:0.2}
100% {opacity:0}
}
@keyframes close-eye {
0% {height: 40px;margin-top: auto;overflow: auto;}
5% {height: 2px;margin-top: 20px;overflow: hidden;}
5.1% {height: 40px;margin-top:0;overflow:visible;}
}
</style>
</head>
<body>
<div class="face">
<div class="forhead"></div>
<div class="cheeks"></div>
<div class="ear"></div>
<div class="eyebrow left"></div>
<div class="eyebrow right"></div>
<div class="eye left"></div>
<div class="eye right"></div>
<div class="mouth"></div>
<div class="shy"></div>
</div>
</body>
</html>
Start with simplifying the equation :-
=》 \tt{a^{4} - ( b + c )^{4}}a
4
−(b+c)
Simplify it further :-
=》 \tt{(a^{2})^{2} - ((b+c)^{2})^{2} }(a
2
−((b+c)
Let ( b + c ) = y
=》 \tt{(a^{2})^{2} - (y^{2})^{2}}(a
Identity going to be used -
a^{2} - b^{2} = (a-b)(a+b)a
=(a−b)(a+b)
Use it there :-
=》 \tt{( a^{2} + y^{2} ) ( a^{2} - y^{2} )}(a
Again, use the same identity :-
=》 \tt{( a^{2} + y^{2}) ( a + y )( a - y)}(a
)(a+y)(a−y)
Now, put the value of y = ( b + c )
=》 \tt{( a^{2} + ( b + c)^{2} ) ( a + ( b + c))( a - (b + c))}(a
2
+(b+c)
2
)(a+(b+c))(a−(b+c))
Now, open the brackets :-
=》 \tt{( a^{2} + ( b +c)^{2})( a + b + c )( a - b - c)}(a
)(a+b+c)(a−b−c)
Identity to be used -
(a + b)^{2} = a^{2} + b^{2} +
Use it and this will be your final step :-
=》 \tt{(a^{2} + b^{2} + c^{2} + 2bc )( a + b + c )( a - b - c )}(a
+2bc)(a+b+c)(a−b−
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